UEFA, the cartel that runs European soccer, came up with the idea of a competition for the champions of European domestic leagues. The competition was known as the European Champions Cup until the mid-nineties, when the competition was reformed as the Champions League to take advantage of the globalization of the sport and the growing television networks that needed things to broadcast.

Year    Winner                Country      Runner-Up                Country
1955/56 Real Madrid           (Spain)      Reims                    (France)
1956/57 Real Madrid           (Spain)      Fiorentina               (Italy)
1957/58 Real Madrid           (Spain)      AC Milan                 (Italy)
1958/59 Real Madrid           (Spain)      Reims                    (France)
1959/60 Real Madrid           (Spain)      Eintracht Frankfurt      (Germany)
1960/61 Benfica               (Portugal)   Barcelona                (Spain)
1961/62 Benfica               (Portugal)   Real Madrid              (Spain)
1962/63 AC Milan              (Italy)      Barcelona                (Spain)
1963/64 Internazionale        (Italy)      Real Madrid              (Spain)
1964/65 Internazionale        (Italy)      Benfica                  (Portugal)
1965/66 Real Madrid           (Spain)      Partizan Belgrade        (Yugoslavia)
1966/67 Celtic                (Scotland)   Internazionale           (Italy)
1967/68 Manchester United     (England)    Benfica                  (Portugal)
1968/69 AC Milan              (Italy)      Ajax                     (Holland)
1969/70 Feyenoord             (Holland)    Celtic                   (Scotland)
1970/71 Ajax                  (Holland)    Panathinaikos            (Greece)
1971/72 Ajax                  (Holland)    Internazionale           (Italy)
1972/73 Ajax                  (Holland)    Juventus                 (Italy)
1973/74 Bayern München        (Germany)    Atlético Madrid          (Spain)
1974/75 Bayern München        (Germany)    Leeds United             (England)
1975/76 Bayern München        (Germany)    St-Etienne               (France)
1976/77 Liverpool             (England)    Borussia Mönchengladbach (Germany)
1977/78 Liverpool             (England)    Club Brugge              (Belgium)
1978/79 Nottingham Forest     (England)    Malmö FF                 (Sweden)
1979/80 Nottingham Forest     (England)    Hamburg SV               (Germany)
1980/81 Liverpool             (England)    Real Madrid              (Spain)
1981/82 Aston Villa           (England)    Bayern München           (Germany)
1982/83 Hamburger SV          (Germany)    Juventus                 (Italy)
1983/84 Liverpool             (England)    AS Roma                  (Italy)
1984/85 Juventus              (Italy)      Liverpool                (England)
1985/86 Steaua Bucuresti      (Romania)    Barcelona                (Spain)
1986/87 Porto                 (Portugal)   Bayern München           (Germany)
1987/88 PSV Eindhoven         (Holland)    Benfica                  (Portugal)
1988/89 AC Milan              (Italy)      Steaua Bucuresti         (Romania)
1989/90 AC Milan              (Italy)      Benfica                  (Portugal)
1990/91 Crvena Zvezda         (Yugoslavia) Olympique Marseille      (France)
1991/92 Barcelona             (Spain)      Sampdoria                (Italy)
1992/93 Olympique Marseille   (France)     AC Milan                 (Italy)
1993/94 AC Milan              (Italy)      Barcelona                (Spain)
1994/95 Ajax                  (Holland)    AC Milan                 (Italy)
1995/96 Juventus              (Italy)      Ajax                     (Holland)
1996/97 Borussia Dortmund     (Germany)    Juventus                 (Italy)
1997/98 Real Madrid           (Spain)      Juventus                 (Italy)
1998/99 Manchester United     (England)    Bayern München           (Germany)
1999/00 Real Madrid           (Spain)      Valencia                 (Spain)
2000/01 Bayern München        (Germany)    Valencia                 (Spain)
2001/02 Real Madrid           (Spain)      Bayer Leverkusen         (Germany)

Acknowledgements: rsssf.com