<PAGE>   1
 
                                                                      EXHIBIT 21
 
Significant subsidiaries of the Corporation at December 31, 1995 were as
follows:
 
                           SUBSIDIARIES OF REGISTRANT
 
<TABLE>
<CAPTION>
                                                                                  JURISDICTION               INCORPORATED/
                                                                                       OF         PERCENT     ACQUIRED BY
                         NAME                             NATURE OF BUSINESS      INCORPORATION    OWNED         GROUP
------------------------------------------------------  -----------------------  ---------------  -------    -------------
<S>                                                     <C>                      <C>              <C>        <C>
General Re Corporation                                  Holding Company          Delaware           N/A       1980
  General Reinsurance Corporation                       Reinsurer                Delaware           100       1970
    Elm Street Corporation                              Real Estate              Delaware           100       1981
    General Star Indemnity Company                      Insurer                  Connecticut        100       1967
    General Star National Insurance Company             Insurer                  Ohio               100       1864/1985
    General Star Management Company                     Management               Delaware           100       1979
    Genesis Underwriting Management Company             Management               Delaware           100       1988
      Broker Markets Agency, Inc.                       Agent                    Connecticut        100       1987
    Genesis Insurance Company                           Insurer                  Connecticut        100       1976/1989
    Genesis Indemnity Insurance Company                 Insurer                  North Dakota       100       1989
    GRC Realty Corporation                              Real Estate              Connecticut        100       1972
    Gen Re Holdings, Inc.                               Holding Company          Delaware           100       1981
      Reinsurance Underwriting Services Limited         Manager                  UK                 100       1966
         General Re Europe Limited                      Reinsurer                UK                 100       1981
         General Re, Correduria de Reaseguros, S.A.     Intermediary             Spain              100(1)    1987
    General and Cologne Re Management Limited           Management               Australia           50(4)    1995
    General Reinsurance Australasia Limited             Reinsurer                Australia          100       1961
      Recoa Investments Pty. Limited                    Investment Company       Australia          100       1967
    General Re Compania de Reaseguros, S.A.             Reinsurer                Uruguay            100       1990
      Mandataria General Re, S.A.                       Agent                    Argentina          100(1)    1990
      General Re Compania de Reaseguros, S.A.           Reinsurer                Argentina          100(1)    1991
  North Star Reinsurance Corporation                    Reinsurer                Delaware           100       1956/1996
  General Re-New England Asset Management, Inc.         Investment Adviser       Delaware           100       1984/1995
  North Star Syndicate, Ltd.                            Insurance Syndicate      Delaware           100       1979
  United States Aviation Underwriters, Inc.             Manager                  New York           100       1928/1982
    USAU Reinsurance Limited                            Reinsurer                Bermuda            100       1978
    Canadian Aviation Insurance Managers Ltd.           Manager                  Montreal, Can.     100       1937
      Airsurance Limitee                                Manager                  Montreal, Can.     100       1982
  General Re Services Corporation                       General Business Corp.   Delaware           100       1979
    General Re Financial Products (Japan) Inc.          Agent/Swap Dealer        Delaware           100       1990
  Herbert Clough Inc.                                   Intermediary             New York           100       1926/1928
  Genplus Managers, Inc.                                Manager                  Delaware           100       1984
  Cresset Capital Limited Partnership                   Venture Capital          NY Partnership      50(2)    1989
  GRD Corporation                                       General Business Corp.   Delaware           100       1987
    General Re-CKAG Reinsurance and Investment S.a
      r.l.                                              Holding Company          Luxembourg        50.1       1994
      Kolnische Ruckversicherungs-Gesellschaft AG       Reinsurer                Germany             75(6)    1846/1994
         Cologne Holding Company of America             Holding Company          Connecticut        100       1992/1994
         Cologne Re Managers Corporation                Management               Delaware           100       1995
         Cologne Reinsurance Company of America         Reinsurer                Connecticut        100       1975/1994
      Cologne Life Reinsurance Company                  Reinsurer                Connecticut        100       1967/1994
         U.S. Health & Life Insurance Company           Insurer                  Delaware           100       1982/1994
         Idealife Insurance Company                     Insurer                  Connecticut        100       1981/1994
      Europa Ruckversicherung AG                        Reinsurer                Germany             84       1947/1994
      Kolnische Versicherungs-Beratungs-und Service
         GmbH                                           General Business Corp.   Germany            100       1988/1994
      The Cologne Reinsurance Company Ltd.              Reinsurer                UK                 100       1983/1994
      Cologne Reinsurance Company Ltd.                  Reinsurer                Ireland             99       1990/1994
      LaKolnische Italia Servizi Riassicurativi SRL     Agent                    Italy              100       1989/1994
      Kolnische Nordiska Aktiebolag                     Insurer                  Sweden             100       1980/1994
      Cologne Reinsurance Finance Holdings B.V.         Holding Company          Netherlands        100       1976/1994
      Cologne Reinsurance Company Ltd.                  Reinsurer                Bermuda            100       1980/1994
         Cologne Reinsurance Ltd.                       Reinsurer                Barbados            75(3)    1989/1994
      LaKolnische Latina S.A.                           Agent                    Mexico              95       1976/1994
      Kolnische Ruck Wien                               Reinsurer                Austria             70(5)    1869/1994
</TABLE>
<PAGE>   2
 
<TABLE>
<CAPTION>
                                                                                  JURISDICTION               INCORPORATED/
                                                                                       OF         PERCENT     ACQUIRED BY
                         NAME                             NATURE OF BUSINESS      INCORPORATION    OWNED         GROUP
------------------------------------------------------  -----------------------  ---------------  -------    -------------
<S>                                                     <C>                      <C>              <C>        <C>
      Cologne Reinsurance Company of South Africa Ltd.  Reinsurer                South Africa        99       1966/1994
      General and Cologne Re Management Limited         Management               Australia           50(4)    1995
      Cologne Life Reinsurance Company of Australia
         Ltd.                                           Reinsurer                Australia           99       1983/1994
      Cologne Reinsurance Consultants Ltd.              General Business Corp.   Hong Kong           99       1987/1994
      Die Kolnische Ruck Riga GmbH                      Agent                    Latvia             100       1990/1994
      LaKolnische Iberica S.A.                          Agent                    Spain              100       1981/1994
      Kolnische Ruck Buenos Aires S.A.                  Agent                    Argentina          100       1992/1994
    General Re London Limited                           General Business Corp.   UK                 100       1992/1994
  GRD Global, Inc.                                      Management               Delaware           100       1995
  General Re Financial Products Corporation             Swap Dealer              Delaware           100       1990
    General Re Financial Products (Canada) Limited      Agent                    Ontario            100       1993
  General Re Financial Products Limited                 Agent                    UK                 100       1990
  General Re Financial Securities Limited               Swap Dealer              UK                 100       1992
  General Re Securities Corporation                     Broker-Dealer            Delaware           100       1991
  General Re Underwriting Services Limited              Underwriting Services    Bermuda            100       1993
  General Re Bermuda, Ltd.                              Reinsurer                Bermuda            100       1993
  General Re T K, Inc.                                  General Business Corp.   Delaware           100       1994
  General Re Strategic Solutions, Inc.                  General Business Corp.   Delaware           100       1995
</TABLE>
 
---------------
(1) Percentages exclude any director qualifying shares
 
(2) Partnership Percentage
 
(3) Cologne Reinsurance Company Ltd. (Bermuda) owns 75 percent and Cologne Life
     Reinsurance Company (Connecticut) owns 25 percent of Cologne Reinsurance
     Ltd. (Barbados)
 
(4) General Reinsurance Corporation and Kolnische Ruchversicherungs-Gesellschaft
     AG each own 50 percent of General and Cologne Re Management Limited
 
(5) Kolnische Ruckversicherungs-Gesellschaft AG owns 70 percent and Wiener
     Stadtische Allgemeine Versicherung Aktiengesellschaft and
     Versicherungsanstalt der osterreichischen Bundeslander
     Versicherungsaktiengesellschaft each own 15 percent of Kolnische Ruck Wien
 
(6) GRD Corporation owns an additional 6.9 percent of Kolnische
     Ruckversicherungs-Gesellschaft AG directly Indentation Shows Ownership)