Well, I like pretty much every genre besides hip hop. It's not that I think it's evil or bad or anything, I just can't relate to it. My favorite bands fall in to two groups: Country and Classic Rock. I'm not sure how I've amalgamated those two styles in my head, but I really like them both.
Country:
Reckless Kelly - Alternative Country, which means that they've sacrificed any chance of being rich and famous for artistic integrity. Really, they're country rock, and would have been called a rock band thirty years ago. I honestly think they might be the most unappreciated band of our generation.
Some Reckless Kelly tracks (the good ones aren't on youtube, sadly):
[yt=Seven Nights in Eire]VnCKG97O4I4[/yt]
[yt=1952 Vincent Black Lightning]hlylarCRayI[/yt]
[yt=How was California?]AMxGp_isIAQ[/yt]
Like I said, their best tunes aren't on youtube, so consider you're listening to their B material, but it's pretty good nonetheless.
Classic Rock:
The Who. I have no idea why I like this band so much, but they just seem to 'get it'. When people talk about the holy trinity of rock and roll, it's The Beatles, The Stones, and The Who (who are considered the holy ghost). I couldn't agree more. Probably the prototypical rock and roll band.
Also, I'm a huge fan of the Eagles, who are really neither rock and roll or country.
