Not that I listen to them but Sigur Ros don't sing using any words at all, they use vocals primarily as an instrument.
I listen to alot of bands that sing in german, KMFDM (Partly English), Joachim Witt, Rammstein, Hanzel und Gretyl, Sopor Aeternus & The Ensemble of Shadows.
Theatre of Tragedy sings in a form of old english.
Japanese bands I like are, Moi dix Mois, Malice Mizer, D'espairs Ray and I like some music by a solo artist (Yasushi Ishii) who does the music for Hellsing.
A Mexican band called Hocico that sings in Spanish and partly in English.
Oh and Rammstein is Tanz Metal not Industrial Metal (Tanz meaning Dance) they sound nothing like Ministry which is Industrial Metal they sound more like Joachim Witt.
Origa a Russian pop artist. (Did a song for the Soundtrack for Ghost in the Shell Stand Alone Complex).
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"They do, but what do you think is on the radio? Meat sounds. You know how when you slap or flap meat, it makes a noise? They talk by flapping their meat at each other. They can even sing by squirting air through their meat." - Terry Bisson