My hands-down first choice would have been Bob Dylan, but I also find it very easy to recognize Don McLean.
I’m glad to see a good response to my OP (nothing more depressing than seeing what you think is a great topic sink like a stone with no replies).
But I’m feeling old. About half of the names on your list I’ve never heard of.
Macy Gray
Tom Waites and Ofra Haza
Judy Garland
Elton John
William Shatner
Tom Waits, David Sylvian.
the guy from the b-52’s. although he was generally a talker, not a singer…but still
eminem, also not much singing, but he has on occasion.
bernadette peters definitely.
cher
ewan mcgregor, too, actually.
nathan lane
Neko Case
Kay Hanley from Letters to Cleo
Johnny Cash
Elvis Costello.
Of course, my answer to almost everything is Elvis Costello. 
Billy Joe Armstrong (Greenday)
The singer from Mindless Self Indulgence
Toni Childs - as one of our local critics said: “she sounds like she’s singing with a lobster halfway down her throat”.
Have to agree with Yeticus Rex about Ozzy.
But it is his speaking voice that really gets me. My dad asked me the other day just what the hell was wrong with him.
“Sheets of LSD?” was the only thing I could think of to say.
Fred Schneider. It’s true, what he does is very distinctive.
Which makes me think of Jello Biafra. He sang more than Schneider does, and even though mentioning one brought the other to mind, if you know Jello’s voice, you won’t confuse it with anybody else’s.
Geddy Lee with a doubt.
You’re all wrong.
Blossom Dearie
She did Figure Eight and Unpack Your Adjectives for Schoolhouse Rock, but she’s also been a cabaret singer for years and years. You hear that voice one time, and you know it for life.
Grr, I meant “Geddy Lee without a doubt”
Peter Hammill
Iris Dement
Janis Joplin definately.
For the guys, Brain Molko of Placebo. Growl.