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...