Other than football, my teams suck right now. It's hard to hate a rival when there's no rivalry.
MLB
Red Sox - I'm sick of hearing about them 24/7 around here
Braves - Those late 90s teams always mopped up with the Mets, plus add John Rocker to the mix. I still don't like that team.
NBA
I'm a Knicks fan, so any of those good rivalries in the 90s - Bulls, Pacers, Heat. I hated all those teams at the time. Now I just hate the Knicks for being a joke.
NFL
Indy is the Pats biggest rival, but I don't really despise them. Probably the NY teams are the ones I can't stand, for a funny reason. They both sucked when I was growing up, and since we had 2 teams, you were stuck with a shitty game at both 1 and 4. So instead of Miami-Buffalo followed by Dallas-San Fran when those were top teams, you got the Jets-Bengals at 1, follwed by Giants-Cardinals at 4. We never got the good games.