I would dare say that I listen to the 'alternative' genres far more than I do classical. Of these I rather enjoy . . .
-Metal - Various styles, but I generally draw the heavyness line a little bit before Meshuggah. I like the more melodic metal ala an Opeth, Lamb of God, or Metallica. Black Sabbath, Megadeth, and Pantera are some other favourites.
-"Prog" - Robert Fripp, particularly as a member of King Crimson, is a personal favourite. Dream Theater is similarly awesome. Brian Eno has his moments.
-Pop - I'm especially partial to the 80's brand of it. Prince is a personal hero, Michael Jackson would be if he could keep his hands to himself. David Bowie, absolute yes. Recently Gnarls Barkley, The Gorillaz, and select singles have caught my attention. Disco is also fun to listen to.
-Heavier Rock - Once it stops sounding like country, I start getting interested. Led Zeppelin comes to mind along with Guns 'n' Roses.
-Electronica - I don't listen to the genre that much, but I can enjoy it a great deal. The Orb's dancier songs, and a lot of the Prodigy's material hit the spot for me. Aphex Twin can be fun too.
-Folk - A very rare indulgence, and I generally only listen when it's mixed with some other genre. Van Morrison is a favourite.
-Video Game Music - Not a genre, but probably the category of music I listen to more often than not. Sakuraba, Uematsu, and Mitsuda have had a large part in sculpting my musical style.
-Jazz - I don't listen often, but when I do, I really enjoy myself. I need to check out more stuff.
-Modern Rock - Not a lot from this category that I like. Mostly the retro bands like The Hives and the White Stripes grab my attention. The Red Hot Chilli Peppers are often sweet as well, Wolfmother is a pretty neat up and coming group, Modest Mouse and Franz Ferdinand occasionally hit the spot for me too.
That's the short list of it all. There's more stuff that I listen to that I wouldn't know how to classify or just can't think of right now.