I'm going to attempt to do what Rex did for the 1964 through 1969 series.
1964 - Yanks over Cards in 7 (iirc) I remember Ken Boyer hitting a grand slam to win one game 4-3. The Cards were down 3-0 when he hit it.
1965 - Dodgers over Twins ... This was thumping Twins team with Allison, Killebrew, Mincher, Battey, Oliva ... but was shut down by Koufax, Drysdale and company.
1966 - Orioles with FRobby, BRobby, Boog Powell was in this one and I think they beat LA. But I'm not sure.
1967 - Like 1964, a heart breaker year for ChiSox fans. Cards over RedSox.
1968 - Tigers over Cards in 7. McClain won 31 games that year, but Mickey Lolich won 3 games in the Series. Gibson K'd 17 batters in one game to set WS record which, I believe, still stands.
1969 - Amazing Mets over Orioles. That year is infamous in Chicago for some reason.