I know this is kind of random, but whenever I listen to Evanescence, I think...Raistish music. Then I got to thinking about what other bands the different characters would like. Here's what I came up with.
Raistlin: Evanescence, Coldplay
Caramon: Journey, Phil Collins
Tanis: America, Enya, Yanni
Sturm: Sting
Flint: .38 Special
Tas: The Beatles
Kit: Foreigner

I don't feel like I would know the other characters good enough, though Goldmoon would probably like Leann Rimes or something.
Anybody else got suggestions? I would advise against putting something like "Distrubed or Godsmack" for Raistlin, because, even though we all know he is distrurbed, I think that kind of music would be too loud, with too much screaming for his personality. I chose Evanescence because it's sort of dark and quiet, sneaking up on you like he does.
Also, I know most of the bands I came up with are from the 80's... but so are they...