Anúna - An Irish choir band that deserves more recognition for its excellent abilities. Not all people like music that sounds as if it belongs in a church, but some of their songs are quite beautiful and moving.
Lene Marlin - Not a band, but an artist. I'm including her anyway, though. She had a great run back in 1998, and her album was simply marvellous. Unfortunately, nobody really took any notice of her, and she quickly faded into obscurity. Edit: After a bit of thought, I decided to check up on Ms. Marlin, and I discovered that she'd released an album at the end of last year. I then went ahead and bought it. Heh - if it hadn't have been for this thread, I wouldn't have known about that.
Funnily enough, I can't think of any others right now. :/