<PAGE>   1





                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C.  20549

                                   FORM 10-Q

(Mark One)


[X]      QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
         EXCHANGE ACT OF 1934

For the quarterly period ended             March 31, 1995
                               ---------------------------------------------- 
                                   or

[  ]     TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
         EXCHANGE ACT  OF 1934

For the transition period from _____________________ to _____________________

Commission File Number                 1-9518
                       ------------------------------------------------------

                 THE PROGRESSIVE CORPORATION            
- -----------------------------------------------------------------------------
  (Exact name of registrant as specified in its charter)

             Ohio                                  34-0963169
- -----------------------------------------------------------------------------
(State or other jurisdiction of                (I.R.S. Employer
incorporation or organization)                Identification No.)

6300 Wilson Mills Road, Mayfield Village, Ohio                44143
- -----------------------------------------------------------------------------
(Address of principal executive offices)                    (Zip Code)

                                (216) 461-5000
- -----------------------------------------------------------------------------
            (Registrant's telephone number, including area code)

        Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 
1934 during the preceding 12 months (or for such shorter period that the 
registrant was required to file such reports), and (2) has been subject to 
such filing requirements for the past 90 days.
                                                  Yes  X  No 
                                                      ---    ---

        Indicate the number of shares outstanding of each of the issuer's 
classes of common stock, as of the latest practicable date.

Common Shares, $1.00 par value: 71,835,953 outstanding at April 28, 1995





                                       1

<PAGE>   2

                         PART I - FINANCIAL INFORMATION
                         ------------------------------

ITEM 1.  Financial Statements

The Progressive Corporation and Subsidiaries
CONSOLIDATED STATEMENTS OF INCOME
(unaudited)


<TABLE>
<CAPTION>
 Three months ended March 31,                                    1995             1994              % Change
- ------------------------------------------------------------------------------------------------------------
 (millions - except per share amounts)
<S>                                                             <C>              <C>                     <C>
 NET PREMIUMS WRITTEN                                            $686.9           $558.2                 23
                                                                 =======================
 REVENUES
 Premiums earned                                                 $624.3           $478.7                 30
 Investment income                                                 44.8             36.8                 22
 Net realized gains (losses) on security sales                     15.4             (2.6)                --
 Service revenues                                                   9.3              9.5                 (2)
                                                                 -----------------------
   Total revenues                                                 693.8            522.4                 33
                                                                 -----------------------

 EXPENSES
 Losses and loss adjustment expenses                              436.9            309.0                 41
 Policy acquisition costs                                         106.6             87.1                 22
 Other underwriting expenses                                       44.0             38.9                 13
 Investment expenses                                                2.1              2.1                 --
 Service expenses                                                   8.4              8.1                  4
 Interest expense                                                  14.3             13.5                  6
                                                                 -----------------------
   Total expenses                                                 612.3            458.7                 33
                                                                 -----------------------


 NET INCOME
 Income before Federal income taxes                                81.5             63.7                 28
 Provision for Federal income taxes                                20.8             15.6                 33
                                                                 -----------------------
 Net income                                                      $ 60.7           $ 48.1                 26
                                                                 =======================

 PER SHARE
   Primary                                                       $  .79           $  .62                 27
   Fully diluted                                                    .79              .62                 27
 WEIGHTED NUMBER EQUIVALENT SHARES
   Primary                                                         74.0             74.5                 (1)
   Fully diluted                                                   74.1             74.5                 (1)





See notes to consolidated financial statements.
</TABLE>






                                       2

<PAGE>   3
The Progressive Corporation and Subsidiaries
CONSOLIDATED BALANCE SHEETS
(unaudited)

<TABLE>
<CAPTION>
                                                                              March 31,                 December 31,
                                                                 --------------------------------------------------
                                                                    1995                1994                 1994
 ------------------------------------------------------------------------------------------------------------------
 (millions)
<S>                                                               <C>                 <C>                  <C>
 ASSETS
 Investments:
 Held-to-maturity:
   Fixed maturities, at amortized cost (market:
     $329.0, $358.8 and $343.8)                                   $  321.0            $  346.9             $  337.6
 Available-for-sale:
   Fixed maturities, at market (amortized cost:
     $2,219.0, $1,963.3 and $2,129.7)                              2,201.8             1,969.3              2,087.0
   Equity securities, at market
     (cost: $434.4, $461.7 and $481.0)                               439.4               472.8                476.3
 Short-term investments, at amortized cost
     (market: $298.5, $299.8 and $279.2)                             298.5               299.8                279.1
                                                                 --------------------------------------------------
       Total investments                                           3,260.7             3,088.8              3,180.0
 Cash                                                                 15.2                17.7                 13.4
 Accrued investment income                                            36.5                36.6                 43.4
 Premiums receivable, net of allowance
   for doubtful accounts of $16.4, $8.9 and $15.6                    574.4               421.4                542.4
 Reinsurance recoverables                                            387.7               407.3                379.7
 Prepaid reinsurance premiums                                         77.0                87.8                 83.2
 Deferred acquisition costs                                          170.9               138.4                161.6
 Federal income taxes                                                 88.4                76.2                103.2
 Property and equipment, net of accumulated
   depreciation of $121.4, $108.5 and $116.7                         149.2               116.9                143.3
 Other assets                                                         90.9                24.5                 24.9
                                                                 --------------------------------------------------
       Total assets                                               $4,850.9            $4,415.6             $4,675.1
                                                                 ===================================================
 LIABILITIES AND SHAREHOLDERS' EQUITY
 Unearned premiums                                                $1,093.1            $  854.7             $1,036.7
 Loss and loss adjustment expense reserves                         1,486.0             1,389.9              1,434.4
 Policy cancellation reserve                                          43.3                56.3                 47.3
 Accounts payable and accrued expenses                               310.9               422.1                329.2
 Funded debt                                                         675.7               675.4                675.6
                                                                 --------------------------------------------------
       Total liabilities                                           3,609.0             3,398.4              3,523.2
                                                                 --------------------------------------------------
 Shareholders' equity:
   9 3/8% Serial Preferred Shares, Series A (issued
     and outstanding, 3.5, 3.6 and 3.5)                               85.8                87.0                 85.8
   Common Shares, $1.00 par value (treasury shares of
     11.2, 10.1 and 11.2)                                             71.8                72.1                 71.2
   Paid-in capital                                                   368.9               359.2                357.1
   Net unrealized appreciation (depreciation) on
     investment securities                                            (7.9)               11.1                (30.7)
   Retained earnings                                                 723.3               487.8                668.5
                                                                 --------------------------------------------------
       Total shareholders' equity                                  1,241.9             1,017.2              1,151.9
                                                                 --------------------------------------------------
         Total liabilities and shareholders' equity               $4,850.9            $4,415.6             $4,675.1
                                                                 ===================================================

See notes to consolidated financial statements.
</TABLE>






                                       3

<PAGE>   4

<TABLE>
The Progressive Corporation and Subsidiaries
CONSOLIDATED STATEMENTS OF CASH FLOWS
(unaudited)

<CAPTION>
 Three months ended March 31,                                            1995                      1994
- -------------------------------------------------------------------------------------------------------
 (millions)
<S>                                                                  <C>                         <C>
 CASH FLOWS FROM OPERATING ACTIVITIES
   Net income                                                        $  60.7                     $ 48.1
   Adjustments to reconcile net income to net cash provided
     from operating activities:
     Depreciation and amortization                                       4.8                        4.0
     Net realized (gains) losses on security sales                     (15.4)                       2.6
     Changes in:
       Unearned premiums                                                56.4                       82.7
       Loss and loss adjustment expense reserves                        51.6                       41.3
       Accounts payable and accrued expenses                           (12.5)                      30.3
       Policy cancellation reserve                                      (4.0)                      (3.8)
       Prepaid reinsurance                                               6.2                       (3.2)
       Reinsurance recoverables                                         (8.0)                     (26.4)
       Premiums receivable                                             (32.0)                     (40.8)
       Deferred acquisition costs                                       (9.3)                     (13.8)
       Federal income taxes                                              2.4                       14.2
       Other, net                                                        8.8                        6.8
                                                                     ----------------------------------
         Net cash provided by operating activities                     109.7                      142.0
 CASH FLOWS FROM INVESTING ACTIVITIES
   Purchases:
     Held-to-maturity:  fixed maturities                                  --                      (46.3)
     Available-for-sale: fixed maturities                             (752.9)                    (429.5)
                        equity securities                             (249.8)                     (54.5)
   Sales:
     Available-for-sale: fixed maturities                              510.8                      137.4
                        equity securities                              297.2                       28.7
   Maturities, paydowns, calls and other:
     Held-to-maturity:  fixed maturities                                16.0                        8.1
     Available-for-sale: fixed maturities                              164.4                       79.6
   Net purchases of short-term investments                             (19.4)                     (69.0)
   (Receivable) payable on securities                                  (68.9)                      36.2
   Purchase of property and equipment                                  (11.6)                     (14.7)
                                                                     ----------------------------------
         Net cash used in investing activities                        (114.2)                    (324.0)
 CASH FLOWS FROM FINANCING ACTIVITIES
   Proceeds from exercise of stock options                               6.3                        1.0
   Tax benefits from exercise of stock options                           6.1                         --
   Proceeds from funded debt                                              --                      198.4
   Payments on funded debt                                               (.1)                       (.2)
   Dividends paid to shareholders                                       (6.0)                      (5.7)
   Acquisition of treasury shares                                         --                       (2.5)
                                                                     ----------------------------------
         Net cash provided by financing activities                       6.3                      191.0
                                                                     ----------------------------------
   Increase in cash                                                      1.8                        9.0
   Cash, January 1                                                      13.4                        8.7
                                                                     ----------------------------------
   Cash, March 31                                                    $  15.2                     $ 17.7
                                                                     ==================================
See notes to consolidated financial statements.
</TABLE>






                                       4

<PAGE>   5
The Progressive Corporation and Subsidiaries

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
(unaudited)



         NOTE 1  Supplemental Cash Flow Information -- The Company paid Federal
income taxes of $6.5 million and $0 for the periods ended March 31, 1995 and
1994, respectively.  Total interest paid was $6.6 million and $5.1 million for
the periods ended March 31, 1995 and 1994, respectively.

         NOTE 2  On March 31, 1995, the Company paid a quarterly dividend of
$.055 per Common Share and a regular quarterly dividend of approximately $.59
per share on the 9 3/8% Serial Preferred Shares, Series A, to shareholders of
record as of the close of business on March 10, 1995.  Both dividends were
declared by the Board of Directors on February 10, 1995.

On April 28, 1995, the Board of Directors declared a quarterly dividend of
$.055 per Common Share and a regular quarterly dividend of approximately $.59
per share on the 9 3/8% Serial Preferred Shares, Series A.  Both dividends are
payable June 30, 1995, to shareholders of record as of the close of business on
June 9, 1995.

         NOTE 3  The financial statements reflect all normal recurring
adjustments which were, in the opinion of management, necessary to present a
fair statement of the results for the interim periods.  The results of
operations for the period ended March 31, 1995 are not necessarily indicative
of the results expected for the full year.





                                       5

<PAGE>   6

I
TEM 2.  Management's Discussion and Analysis of Financial
         Condition and Results of Operations.



RESULTS OF OPERATIONS

For the first quarter 1995, operating income, which excludes net realized gains
and losses on security sales, was $50.7 million, or $.66 per share, compared to
$49.8 million, or $.64 per share, last year.  The combined ratio was 94.1,
compared to 90.9 for the first quarter 1994.

Net premiums written increased 23% over the first quarter 1994, primarily
reflecting unit growth in the core automobile insurance business.  This growth
resulted from the Company maintaining competitive rates due to cost control
efforts.  Premiums earned, which are a function of the amount of premiums
written in the current and prior periods, increased 30% for the quarter.
Service revenue decreased 2% to $9.3 million for the quarter.

Claim costs, which represent actual and estimated future payments to or for our
policyholders, as well as loss estimates for future assignments and assessments
under state-mandated assigned risk programs, increased as a percentage of
premiums earned to 70% for the quarter, compared to 65% in 1994.  During the
quarter, the Company raised rates but at a pace slower than its rising loss
costs.  Policy acquisition costs and other underwriting expenses as a
percentage of premiums earned decreased to 24% for the first quarter, compared
to 26% in 1994.  Service expenses increased 4% for the quarter, primarily
reflecting a slight increase in fixed operating expenses.

Recurring investment income (interest and dividends) increased 22% for the
quarter, reflecting an increase in the average investment portfolio and a mix
shift to taxable securities.  The Company had net realized gains on security
sales of $15.4 million for the quarter, compared to net realized losses on
security sales of $2.6 million in the first quarter of 1994.  At March 31, 1995,
the Company's portfolio had $4.2 million in total unrealized losses, compared
to $41.1 million in total unrealized losses at December 31, 1994, primarily
reflecting a general decline in interest rate levels.

The Company continues to invest in fixed maturity, short-term and equity
securities.  The majority of the portfolio ($2,617.0 million, or 80.3%, at
March 31, 1995 and $2,360.8 million, or 76.4%, at March 31, 1994) was in
short-term and intermediate-term, investment-grade fixed-income securities.
Long-term investment-grade fixed-income securities represented $53.7 million,
or 1.6%, and $81.5 million, or 2.7% of the total investment portfolio at March
31, 1995 and 1994, respectively.

As of March 31, 1995 and 1994, the equity portfolio of the Company was $439.4
million, or 13.5%, and $472.8 million, or 15.3%, respectively, of the total
investment portfolio.  The equity portfolio consists of preferred stocks
($266.9 million in 1995 and $360.1 million in 1994), and common stocks ($172.5
million in 1995 and $112.7 million in 1994).  As of March 31, 1995 and 1994,
the non-investment grade fixed-income portfolio of the Company was $150.6
million, or 4.6%, and $173.7 million, or 5.6%, respectively, of the total
investment portfolio.

The Company's financial instruments with off-balance-sheet risk had a net
market value of $(.6) million and $.4 million as of March 31, 1995 and 1994,
respectively.

The weighted average annualized fully taxable equivalent book yield of the
portfolio was 6.8% and 6.5% for the quarters ended March 31, 1995 and 1994,
respectively.

FINANCIAL CONDITION

Progressive's insurance operations create liquidity by collecting and investing
premiums written from new and renewal business in advance of paying claims.
For the three months ended March 31, 1995, operations generated a positive cash
flow of $109.7 million.





                                       6

<PAGE>   7

 
                         PART II - OTHER INFORMATION
                          ---------------------------



ITEM 4.   Submission of Matters to a Vote of Security Holders.

          At the April 28, 1995 Annual Meeting of the Shareholders of the
          Company, 62,019,184 Common Shares were represented in person or by
          proxy.

          The shareholders approved the proposal to fix the number of directors
          at nine.  The proposal received 60,797,276 affirmative votes, 931,173
          negative votes and 290,735 abstentions.

          At the meeting, the shareholders elected the eight directors named
          below, each to serve for a term of one year.  One vacancy remains on
          the Board. The votes cast for each director were as follows:


<TABLE>
          <S>                                                          <C>                    <C>
                                                                       For                    Withheld
                                                                       ---                    --------
          Milton N. Allen                                              61,593,216             425,968
          B. Charles Ames                                              61,604,915             414,269
          Stephen R. Hardis                                            61,618,948             400,236
          Janet Hill                                                   61,602,188             416,996
          Peter B. Lewis                                               61,610,796             408,388
          Norman S. Matthews                                           61,618,101             401,083
          Donald B. Shackelford                                        61,615,008             404,176
          Paul B. Sigler                                               61,598,705             420,479
</TABLE>


          The shareholders approved The Progressive Corporation 1995
          Executive Bonus Plan, which provides certain executive officers of the
          Company with the opportunity to earn performance-based incentive 
          compensation. This proposal received 59,691,280 affirmative votes, 
          1,410,057 negative votes and 917,847 abstentions.

          The shareholders approved The Progressive Corporation Executive
          Deferred Compensation Plan, pursuant to which certain executive
          officers and other key employees of the Company may defer receipt and 
          invest some or all of the incentive compensation that they earn. This
          proposal received 59,219,287 affirmative votes, 1,846,911 negative 
          votes and 952,986 abstentions.

          The shareholders approved the Progressive Corporation 1995
          Incentive Plan, pursuant to which stock options and other stock-based 
          awards may be granted to officers or other key employees of the 
          Company or its subsidiaries. This proposal received 52,774,485 
          affirmative votes, 8,538,173 negative votes and 706,526 abstentions.


ITEM 5.   Other Information.

          On April 28, 1995, Michael C. Murr, the Company's Chief Investment
          and Capital Officer and the President of Progressive Partners, Inc.,
          resigned. 


ITEM 6.   Exhibits and Reports on Form 8-K.

          (a)    Exhibits:

                 See exhibit index on page 9.


          (b)    Reports on Form 8-K during the quarter ended March 31, 1995: 

                 None





                                       7

<PAGE>   8

                                   SIGNATURES
                                   ----------




Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.




                                              THE PROGRESSIVE CORPORATION
                                              ---------------------------
                                              (Registrant)





Date:  May 12, 1995                           BY:  /s/ DAVID M. SCHNEIDER 
     ----------------                             ---------------------------
                                                  David M. Schneider 
                                                  Secretary of the Registrant





Date:  May 12, 1995                           BY:  /s/ CHARLES B. CHOKEL
     ----------------                             --------------------------- 
                                                  Charles B. Chokel 
                                                  Treasurer and Chief Financial 
                                                  Officer of the Registrant





                                       8

<PAGE>   9

                                 EXHIBIT INDEX
                                 -------------


        Exhibit No.      Form 10-Q
         Under Reg.       Exhibit
       S-K, Item 601        No.          Description of Exhibit
       -------------     ---------       ----------------------



            (11)            11           Computation of Earnings Per Share

            (27)            27           Financial Data Schedule

            (99)            99           Computation of Premiums Earned





                                       9





<PAGE>   1
                                 EXHIBIT NO. 11
                                 --------------

                                 COMPUTATION OF


                               EARNINGS PER SHARE

<PAGE>   2

<TABLE>
                                                  THE PROGRESSIVE CORPORATION AND SUBSIDIARIES
                                                        COMPUTATION OF EARNINGS PER SHARE
                                                      (millions - except per share amounts)
                                                                   (unaudited)




<CAPTION>
                                                                  Three Months Ended March 31,
                                                 ----------------------------------------------------------------      
                                                       1995                                      1994
                                                 ---------------------                    -----------------------
                                                                  Per                                        Per
                                                 Amount          Share                    Amount            Share
                                                 ------          -----                    ------            -----
 <S>                                             <C>             <C>                       <C>              <C>
 PRIMARY:
 Net income                                      $60.7                                     $48.1
 Less:  Preferred stock dividends                 (2.1)                                     (2.2)
                                                 ------                                   ------                 
 Income available to Common
   Shareholders                                  $58.6           $.79                      $45.9            $ .62
                                                 ======          =====                    ======            =====

 Average shares outstanding                       71.5                                      72.1
 Net effect of dilutive stock options              2.5                                       2.4
                                                 ------                                   ------                 
     Total                                        74.0                                      74.5
                                                 ======                                   ====== 

 FULLY DILUTED:
 Net income                                      $60.7                                     $48.1
 Less: Preferred stock dividends                  (2.1)                                     (2.2)
                                                 -----                                     -----
 Income available to Common
   Shareholders                                  $58.6           $.79                      $45.9             $ .62
                                                 ======          =====                    ======            =====


 Average shares outstanding                       71.5                                      72.1
 Net effect of dilutive stock options              2.6                                       2.4
                                                 ------                                   ------

     Total                                        74.1                                      74.5
                                                 ======                                   ======
</TABLE>






<TABLE> <S> <C>

<ARTICLE> 7
<LEGEND> 
This schedule contains summary financial information extracted from the
consolidated balance sheets and statements of income and is qualified in its
entirety by reference to such financial statements.
</LEGEND>
<MULTIPLIER> 1,000
       
<S>                             <C>
<PERIOD-TYPE>                   3-MOS
<FISCAL-YEAR-END>                          DEC-31-1995
<PERIOD-START>                             JAN-01-1995
<PERIOD-END>                               MAR-31-1995
<DEBT-HELD-FOR-SALE>                         2,201,800
<DEBT-CARRYING-VALUE>                          321,000
<DEBT-MARKET-VALUE>                            329,000
<EQUITIES>                                     439,400
<MORTGAGE>                                           0
<REAL-ESTATE>                                        0
<TOTAL-INVEST>                               3,260,700
<CASH>                                          15,200
<RECOVER-REINSURE>                             387,700
<DEFERRED-ACQUISITION>                         170,900
<TOTAL-ASSETS>                               4,850,900
<POLICY-LOSSES>                              1,486,000
<UNEARNED-PREMIUMS>                          1,093,100
<POLICY-OTHER>                                       0
<POLICY-HOLDER-FUNDS>                                0
<NOTES-PAYABLE>                                675,700
<COMMON>                                        71,800
<PREFERRED-MANDATORY>                                0
<PREFERRED>                                     85,800
<OTHER-SE>                                   1,084,300
<TOTAL-LIABILITY-AND-EQUITY>                 4,850,900
<PREMIUMS>                                     624,300
<INVESTMENT-INCOME>                             42,700
<INVESTMENT-GAINS>                              15,400
<OTHER-INCOME>                                   9,300
<BENEFITS>                                     436,900
<UNDERWRITING-AMORTIZATION>                    106,600
<UNDERWRITING-OTHER>                            44,000
<INCOME-PRETAX>                                 81,500
<INCOME-TAX>                                    20,800
<INCOME-CONTINUING>                             60,700
<DISCONTINUED>                                       0
<EXTRAORDINARY>                                      0
<CHANGES>                                            0
<NET-INCOME>                                    60,700
<EPS-PRIMARY>                                      .79
<EPS-DILUTED>                                      .79
<RESERVE-OPEN>                                       0
<PROVISION-CURRENT>                                  0
<PROVISION-PRIOR>                                    0
<PAYMENTS-CURRENT>                                   0
<PAYMENTS-PRIOR>                                     0
<RESERVE-CLOSE>
                                      0
<CUMULATIVE-DEFICIENCY>                              0
        

</TABLE>




<PAGE>   1
                                EXHIBIT NO. 99
                                --------------
      
                        COMPUTATION OF PREMIUMS EARNED

<PAGE>   2
                  THE PROGRESSIVE CORPORATION AND SUBSIDIARIES
                         COMPUTATION OF PREMIUMS EARNED
                                   (millions)
                                  (unaudited)






<TABLE>
<CAPTION>
                                                                    Three Months Ended March 31,
                                                        ----------------------------------------------------   
                                                           1995                 1994                % Change
                                                        ----------------------------------------------------   
<S>                                                                                                      <C>
 Total direct premiums written                          $726.0                $605.6                     20

 Reinsurance ceded, net                                  (39.1)                (47.4)                    18
                                                        --------------------------------
 Net premiums written                                    686.9                 558.2                     23

 Change in net unearned premiums(1)                      (62.6)                (79.5)                    21
                                                        --------------------------------

 Premiums earned                                        $624.3                $478.7                     30
                                                        ================================



<FN>
(1) Represents change in unearned premiums net of prepaid reinsurance premiums.
</TABLE>