I listen to classical, rock 'n' roll, heavy metal, alternative, & chillout. & also about 15 more genres of music. But these are the main ones...
Classical - Liszt, Beethoven, Tchaikovsky & the like.
Rock 'n' Roll - Led Zeppelin, The Rolling Stones...
Heavy Metal - Black Sabbath, Iron Maiden, Metallica, Pantera, Damage Plan, Black Label Society, Ozzy Osbourne...
Alternative - Björk
Chillout - Anything that will relax me.
I could go into detail, but that would result in quite a long post, & I don't have enough time...