Russell Mael.
No-one’s mentioned Perry Farrell. I never heard anybody else sing like that.
The guy from The Music has a wierd high pitched voice that fits in nicely with the frankly rocking tunes they do.
Louise Rhodes from Lamb has an affectation to her voice that I know some find really annoying, but I really like
Roison Murphy from Moloko
On the natural side, Blossom Dearie. If you don’t recognize the name, think Unpack Your Adjectives and Figure Eight from Schoolhouse Rock. She’s a serious singer of jazz standards and such, but still in that same girlish voice.
And in a similar vein, Yeardley Smith (who does the voice of Lisa Simpson) has a pretty good set of pipes.
For a processed voice, listen to Laurie Anderson in some of her songs, especially O, Superman. She combines her natural voice with the processors to great effect.
Loudon Wainwright III
One of my first thoughts was David Sedaris’s piece on, as a kid, wanting to sing commercials in the style of Billie Holiday – you have to hear it to believe it.
Leonard Cohen was once described as “having a voice like a burlap bag”, which I find to be a perfect description. I have noticed that as he has aged he has felt the need to add breathy backup singers to many of his songs. Completely ruins it for me. He was one person who could convey great emotion with his voice, and it doesn’t need to be obscured by backup singers.
Roland Gift, lead singer of the 80s band Fine Young Cannibals. I always thought he sounded as if he was singing with his tongue glued to the back of his lower front teeth.
Leonard Cohen is probably my number one pick, followed closely by Tom Waits. I like Dwight Yoakam’s voice, but it’s strange because it’s traditional, which isn’t really popular in mainstream country music anymore.
As for the ladies, I guess Billie Holiday by default because I can’t really think of anyone else at the moment
Bruce Springsteen, whose voice I can’t stand, and Carole King, whose voice I love.
I’m humming the Oscar Meyer jingle as we speak!
Richard Harris
Biff Rose
Jimmy Webb
Without a doubt, the highest voice in Rockdom, does not belong to Getty Lee
With a Power Falsetto,hands down,David SurKamp of Pavlov's Dog.I can’t beleive this thread reached page 2 without mentioning the two craziest voices of 80’s new wave - Talking Heads’ David Byrne and Devo’s Mark Mothersbaugh
Check out the Incredible String Band, jsgoddess. Robin Williamson has a truly strange and wonderful voice (and for some inexplicable reason, whenever I crank up the volume, I wind up getting the whole house to myself).
I’ve always thought Nanci Griffith had a very odd voice.
Very, very nasal. Still love her though.
[QUOTE=koeeoaddi]
Check out the Incredible String Band, jsgoddess./QUOTE]
There are so few things in this world you can count on … koeeoaddi taking an opportunity to plug the Incredible String Band is definitely one of them. 
Cool. Somebody noticed.
::tosses lava lamp, Indian bespread and hookah into knapsack::
My work here is done. 
Done The release date is Oct. 5th from what I’ve heard and read.
Another vote for Thom Yorke.
Roland Orzabal, my usernamesake, has a very distinctive voice as well, though I don’t know if I’d call it strange.
Wait a minute! In what way does Leon Redbone “not sing”?
I love Joe Cocker.
I like Kate Bush except for her voice.
I like Cassandra Wilson, basso contralto & all.
And Macy Gray is cute.
Oh, & I’m that age, you know, where I had a big crush on Cyndi Lauper. Big.