Sigur Ros - Icelandic
“Iceland’s Best Album of the Century”
Experimental Pop Rock?..I haven’t really listened to enough to classify them, but they are pretty widely acclaimed.
And I guess technically it should be “Sigur Rós”
Try Ommadawn by Mike Oldfield. There is not much singing, but what there is is in Gaelic, I believe. (On Horseback, the short fun track three is in English, though.)
Heavy rock/metal industrial?
Rammstein? 
Japanese bands of those genres I recommend: Dir en Grey, Machine, Miyavi, Endorphine, Hakuei. Kagerou’s not bad either.
Malice Mizer actually didn’t do much rock… it’s more baroque/gothic, far from industrial or heavy rock. Gackt is more ethereal / gothic experimental at his best and pop / R&B at his worst.
The Scottish bands Runrig and Capercaillie frequently sing in Gaelic.
[Rammstein hijack]
Some college friends and I listened to lots of Rammstein. Then this “raver chick” started hanging out with us and would say, “You should listen to (list of industrial & metal bands). Rammstein is just a joke band anyway.”
We would usually respond, “that’s why we like them,” and she would get all huffy & stomp off. Guess some people can’t understand other’s tastes.
[/Rammstein hijack]
I was going to recommend Israeli stuff too, but it’s not usually like German rock.
Thanks for the suggestions so far, keep 'em coming! 
I love Rammstein (heck, a Rammstein LiveJournal avatar was what made JarbabyJ find me there!), but I know that a lot of people look down their nose at them. Who cares? I think it’s fun music.
I love these suggestions though! Finnish metal, J-Rock (mmm!), Icelandic pop rock, these are what I’ve been looking for! And I’m using too many exclamation points!
More Israeli stuff would be greatly appreciated, I love what I’ve heard so far. Thanks go to Alessan for telling me the transliterated name of my Israeli band (it’s been driving me nuts since I got it). I eventually want to learn Hebrew, so I figure it’d be good stuff to listen to (my German music’s been helping with my German classes, so who knows?).
Of course I have to jump in and say “musical theatre.” Most shows are done in German, Japanese, and lots of others.
Check out www.eur.com cast database.
Bethlehem’s “Schatten Aus Der Alexander Welt” (review at http://www.ssmt-reviews.com/db/searchrev.php?artistID=134&showReview=true#R367 )
Finntroll’s “Jaktens Tid” (review at http://www.ssmt-reviews.com/db/searchrev.php?artistID=448&showReview=true#R1046 )
I’d like to second the vote for Sigur Rós. It’s really wonderful stuff.
I’d like to second the vote for Sigur Rós. It’s really wonderful stuff.
Well, there tends to be a good deal of crossover in my experience, among goth and industrial fans, so I took it from there.
To go back to the harder stuff (Gods, I feel like we’re talking about drugs…) - though lower on my list, X-Japan isn’t too bad.
Well, they’re not industrial or even rock, but Pink Martini sing in French, English, and Spanish. Good in every language. Sympathique is a great album.
“Das Ich” has some electronic stuff that’s not garbage.
Rajas, a Japanese Hair-Metal band from the 80’s, has recently reunited and released a new album Yuugyou. I wholeheartedly recommend it, and not just because the lead guitarist is my boss.
I mentioned Khaled in another thread, but he’s so good, I want to give him another plug. He’s an Algerian and sings in French. I think the style is called Rai - kind of an Arabic feel, with African and Reggae styles intertwined. And what a voice this guy has. I don’t have a clue what he’s singing about, but as soon as he opens his mouth I am riveted.
Try **N’ssi N’ssi ** and Sahra
Gorky’s Zygotic Mynci are an absolutely wonderful Welsh band with a few songs in Welsh. None on the latest album, sadly, although the EP before contained the haunting “Sbia ar y Seren.” Their collection “Introducing…” has a few Welsh tunes, though. Their style varies a lot although I guess “Introducing…” has the most raucous sound of any of their albums that I have…they’ve veered toward Fairport-style folk in recent years.
Another vote for Sigur Rós. Lead singer Jon Thor Birgisson calls the language he sings in “Hopelandic,” a nonsensical mixture of English, Icelandic, and pure gibberish.
I’m not familiar with much of Cheb Mami’s work (the backing singer on Sting’s “Desert Rose”) but he has one amazing song called “Azwaw” - sung in Arabic, I believe - so I’ll also recommend him.