I listen to a little of everything, really. And now I shall list genres and artists (or albums) to demonstrate:
Rock/Alternative: New Found Glory, Coldplay
Pop: Lady Gaga, Weird Al, Train, Michael Jackson, Simon and Milo
Country: Taylor Swift, Shania Twain, Montgomery Gentry, Garth Brooks
Classic Rock: Beatles, Billy Joel, Paul Williams, Rod Stewart
Metal: Nightwish, Kamelot, Epica, Dragonforce
Game and Film soundtracks: Final Fantasy and Kingdom Hearts soundtracks, the works of Noriyuki Iwadare; Ratatouille, Up, Fantasia, Fantasia 2000, Pride and Prejudice, and Howl's Moving Castle soundtracks.
Musical Soundtracks: Disney Musicals (Beauty and the Beast, Little Mermaid, etc.), The Fiddler on the Roof, Cabaret, the complete Riverdance collection
Celtic/Folk music: Loreena McKennitt, David Arkenstone, Celtic Women, Rob Crabtree, Doug Cameron
Celtic Rock: Enter the Haggis
Hindi: A.R. Rahman
Classical: E.S. Posthumus, Ludovico Einaudi (solo pianist), Richard Joo (performing works composed by Billy Joel, an album called "Billy Joel: Op. 1-10 Fantasies & Delusions - Music for Solo Piano")
World Music: Twelve Girls Band, Bond
Christian/Holiday music: Rachel Lampa, Tait, Natalie Grant, Trans-Siberian Orchestra
Remixes and Tributes: Vitamin String Quartet, OC Remixes, Everlife, MoAbi
Electronic/Electronica: Eiffel 65, CASCADA, Daft Punk, Froggy Mix
New Age: Blue Stone, Achillea, Delerium, Adiemus/Karl Jenkins
Hip-Hop: Black Eyed Peas
J-Rock: Utada Hikaru, Vocaloids
That's sort of a basic summary, but I still have quite a bit that's just sort of pepperings from random artists or genres, and works from unsigned artists like Tay Zonday or Pharaoh Atem (Pharaoh Atem has his own web site, he does remixes and did a lot of work specifically on Final Fantasy XI). Still, there aren't too many genres I don't have at least a little bit from. I guess one would be rap, particularly gangster rap. That's just too far down the rabbit hole (or rather, downward spiral) of hip-hop for my liking.
It's not something I do on purpose, just so I can tell people "But I DO listen to everything," I just grab whatever I think sounds good. And over the years I've discovered my specifications for something being "good" are very flexible.