I've got a lot of range, but I'm pretty picky. For a lot of things, I'll like a song or two by an artist and on occassion I'll like most of an album and a few songs from the artist's other albums
I like Pop, Rock, some limited electronic and trance, some select Country, limited rap, just some dubstep so far (wub wub wub wub), and a lot of things that are lumped under Alternative. I like the more active pieces of classical and soundtrack music. Japanese pop and Anime music? Fuck yes.
Oldies. Oh yes, I like oldies even though they're before even my time.
Anyways, some of the bands and artists that have produced a lot of songs I've liked:
Avenged Sevenfold
Modest Mouse (Good News for People Who Like Bad News)
Pink
No Doubt
Eric Clapton (Unplugged)
Ayumi Hamasaki
My Chemical Romance
Elton John
Nobuo Uematsu
Paramore
Rob Thomas
Ronald Jenkies
Santana
Skillet
Akira Ifukube
The Wallflowers
One Republic
Paramore
Wierd Al