the biggest rivalry in college sports has to be Michigan vs. Ohio State. its always competitive and i think it has had a say in who wins the big ten title something like the past 12 years. i think the series is very close and its one of those where a coach will be fired for losing this game too many times...even if they are good. (see tressel and maybe Carr after this year).other than that i would say Red Sox/ Yankees, Bears/Packers, Pats/Colts and USA/Russia