Lisa Gerrard, Yma Sumak, Cocteau Twins, you guys beat me to my all-time favorites (it is totally sick how many copies of original pressings LPs, 180g LPs, Japanese mini-LP CDs, SACDs copies I collected but not listening to...).
Since Bjork had been mentioned, let me add "Miranda Sex Garden": not exactly EXOTIC singers/dancers but beautiful Goth-oriented Bjork for all of us.
To move this thread off dead-serious Opera/Mid-Eastern direction, let me add
Lene Nystrøm, the lead singer for Aqua: She sounds like a chipmunk on my fav "barbie" tunes, but, unfortunately, her ego got a shot and she decided to go mainstreem, Abba-style and she got Aqua disbanded.