Personally, I don't discriminate when it comes to music and listen to a variety of non metal stuff from...
Indie-Eisely, Modest Mouse, Neutral Milk Hotel, Big Black...
Hardcore-Bane, Shai Hulud, old Poison the Well, Bad Brains, Agnostic Front...
Metalcore/Grind-Between the Buried and Me (though calling them that is a great injustice), Zao, Athena in Hades, Into the Moat...
Post-Hardcore-Hopesfall, Antioch Arrow, Angel Hair...
Pop-The Smiths, Bella and Sebastian, Tori Amos...
Early Post-Punk-Bauhaus, The Cure, Joy Division, Nick Cave and The Bad Seeds...
Punk-The Clash (need I say more), Crucifix, Minor Threat...
New Wave-Japan, The Cure, New Order, Eurythmics...
Dance-Lords of Acid, Ian Van Dahl, Collide...
JPop-Shazna...
Some Rap-A Tribe Called Quest, Atmospere...
Drum & Bass-Reid Speed...
Classic Rock-The Doors, CCR...
Early Grunge-The Smashing Pumpkins, Pearl Jam, Soul Asylum...
Emo/Scremo-Funeral for a Friend, Megans Room, Refused, Grade...
Ska-The Skatellits, Reel Big Fish, Folly...
Reggae-Bob Marley and the Wailers, Steel Pulse...
Funk-Earth Wind and Fire, The Red Hot Chili Peppers...
Blues-Muddy Waters, Tom Waits...
Doowop-The Penguins...
Song Writers-Pat Benitar, Johnny Cash, Willie Nelson, Cyndi Lauper...
...As just a few examples. I know many more and this is just a short list so don't any elitists take it to heart.