I played APBA.... still have a bunch of those cards in the attic. Tilly Shafer was great in the 1912 World Series set... seemed to always get on base, then could run like a rabbit.
A bunch of us played lots of All Star Baseball, it was put out by Avalon Hill as I recall. Simple but fun. We had a league, a WS. Cy Young threw the only no hitter we had, and we must have played a thousand games. He walked 2.
And for our 1948 Indians fan....