Most of the music I like is either older stuff or non-mainstream. I like Talking Heads and Depeche Mode (I'm getting OLD), but I also like ThouShaltNot and Soil & Eclipse.
I'm going to suggest a handful of tunes (and I'll do so every so often); if you have iTunes, you can listen to samples of them in the iTunes Store, or you can try to find samples on Amazon. So, look these up, give them a listen, and if you like them, drop me a comment to let me know?
"Whispering Trees" by Soil & Eclipse (You may have to look them up as Soil and Eclipse, they are listed both ways on both Amazon and iTunes for separate albums, which is kind of annoying).
"Mandalay Bay" by Blackmore's Night
"Over and Done" by Deine Lakaien
"Cardinal Directions" by ThouShaltNot