All genres I don't like. Punk is really fun to play on drums, but I don't really like listening to it if I have a choice. Metalcore just sounds like mutilated, sub-par metal, and Death metal is soooo boring and monotonous.
Depends on the metalcore, really... a lot of it's just god-awful cookie-cutter, and you really have to sift through the garbage, I tend to listen to the music that's more melodic or closer to the hardcoe side of it. I guess if you aren't a punk kinda guy you wouldn't see the appeal, but it's usually quite fun and uplifting.
As for the death metal, it's pretty much the Faceless who put on a good show a couple years ago, and a local melodic death band In Dread Response, who also do a bit if post-metal.
All started with the Skateboard Park Tycoon soundtrack... I didn't like punk as a kid (in fact I didn't listen to any music at all), but the songs were really catchy and I could still remember them years later...