Yoiking (the traditional chanting of the Sami-people):
Mari Boine - "Gula gula" (live, the title is not - as it says in the beginning of the clip - "Goaskinviellja")
Mari Boine - "Gulan du" (not a clip, only music)
Not sure, if it can be considered a special vocal technique/style, but here's a Persian singer:
Sima Bina - "Majnoon naboodam":
Le Mystère Des Voix Bulgares: