No doubt this topic has been covered before, but I used the search feature and couldn't find the right thread. So here it is.
I like punk, classic rock (this basically means the stuff you'd find on oldies stations, without the 60's bubblegum pop, with some Led Zepplin and other 70's hard rockers), Grunge, Parody, any rapper that overlaps into another genre (like the Beastie Boys or Outkast - usually the ones that "hardcore" rappers deem to be fakes, or not ghetto enough), alternative, some heavy metal, and classical, if I'm trying to concentrate on something. I just recently got introduced to progressive metal, like Symphony X (The Odyssey - who'd a-thunkin' you could get a half hour song stuck in your head?) and Dream Theater, and I'm really liking it so far.
I dislike modern country (the stuff that borders on modern pop, like Shania Twain and Tim McGraw), most modern pop, and rappers that are too full of themselves. I also dislike nu-metal, except for System of a Down and Drowning Pool, which I like.
Everything in between is the "if I'm in the mood for it" music.
If ya want to get band specific, here's my favorites:
Red Hot Chili Peppers Incubss Led Zepplin Pink Floyd The Beatles Nirvana The Who