I don't watch the majority of sports, so I'll just list what I do watch.
I'll watch pretty much any NFL game (except preseason) with some level of interest, even if I'm not rooting for a particular team. That's probably the only sport I can say that about. I am very interested in UConn men's basketball and football, and will always watch those games. UConn women's basketball, I'll sometimes watch if it's an interesting/competitive regular season opponent, and I'll always watch tournament games. Related to that, I'll occasionally watch an NBA or WNBA game if there's a UConn alum playing and they're getting court time. UConn baseball or hockey, once in a while if the stakes are high.
I actually like watching the Connecticut Sun a lot now, and find myself watching their games (when on) and rooting for them. I do listen to most of the Yankees games on the radio, because they're rarely on TV (I still haven't tried subscribing to YES). I'm a legit lifelong fan since childhood. I'll watch the Knicks when they're on too, though I'm not really a diehard fan - more of a lifelong casual fan.
When UConn men's basketball is doing well, I'll take an interest in the other Big East games. I have trouble staying focused on other conference games, unless I perceive UConn to gain some benefit based on the outcome (say, moving up in the rankings). UConn football being in no man's land has made me somewhat bitter towards other college football programs, so I don't watch much. Occasionally I'll put a game on TV if it's convenient, but I don't pay close attention.
No Whalers, no hockey.
I'll watch NBA and MLB playoff games not involving the Yankees or Knicks, but rarely ordinary regular season games. World Cup soccer is interesting once they get to the quarterfinals or so. Once in a great while I'll watch figure skating or the Hartford pro soccer team.
I would never, ever watch MMA, boxing, or NASCAR. I find them viscerally unappealing. A close friend of mine loves Formula One, so I'll tolerate it when I'm over his house, but honestly it does nothing for me.