I'll listen to virtually any genre, though here are definitely some I listen to more frequently then others. I'm really partial to folk music, especially. Ani DiFranco, Tegan and Sara, Cat Stevens... I also love Alanis Morisette (though she leans a bit more towards pop than folk).
I also like a mix of alternative, rock, and pop music, though-- Owl City, Superchic[k], Shinedown... seriously, I'm not kidding when I say I'll listen to virtually anything!
(I do tend to stear clear of really heavy metal or harder rap, though. I love hard rock and will listen to some hip hop, but heavy metal and rap aggravate my hypersensitive skull and tend to cause headaches, so it's difficult for me to enjoy them.)