Music styles:
Punk, Emo, Hardcore, Alternative... but really anything besides Rap and most Pop.
Some good bands:
Weezer, NOFX, Saves the Day, Cake, Ataris, AFI, Bracket, Goldfinger, Lagwagon, Jimmy Eat World, and many more.
Some bad bands:
too many.....
actually, I remember I made a list a while ago, because someone asked me a similar question ..
http://www.pubarso.com/bands.shtml