"Raging Bull" for me. Not only the all-time greatest sports movie, but one of the all-time greatest movies, period.

SC's list is pretty good, altho I don't know if pool ("The Hustler") is a sport or a game.

I might throw "Bull Durham" (also with Costner) in there somewhere. Also, "Somebody Up There Likes Me" (1956), the Rocky Graziano story, was very good. Paul Newman, in his third-ever film, gives an excellent performance as Rocky, and Robert Loggia, lately of The Sopranos and well known here as Frank Lopez in "Scarface", makes his film debut.

And if pool is a sport, and poker is also as raggingbull says, then "Rounders" with Matt Damon and Ed Norton would be on my list