Not limited to three- but limited to non-classical
Hmmm let’s see-
Freddie Mercury
Dean Martin( sway):love:
Eddie Vedder
James Taylor
I’m sure y’all will remind me of the ones I’ve forgotten.
Go for it.
He’s not that well-known, but I think Casey Stratton is a good vocalist. He does lots of Tori Amos covers and sounds much like her, too.
http://youtube.com/watch?v=O5-cwgOr2CY
Perhaps on the other end of the male voice-spectrum is Christy Moore. I love him, too. Here he is doing a duet with Sinéad O’Connor (though he has the smaller part; I don’t have any videos of him without Sinéad O’Connor right offhand).
Van Morrison
Roy Orbison
Ray Charles
Dick Gaughan
Baaba Maal
Teddy Taylor
Howard Tate
Marvin Gaye
Youssou N’Dour
Salif Keita
Garnett Mimms
Camaron de la Isla
Elvis Presley
Roger Whitaker
Bobby McFerrin
Joe Cocker
I always thought Paul Robeson had a sweet voice.
I don’t know if you’d call it a “great” voice, but Jimi Hendrix’s singing always really got to me.
If we can consider three separate voices as one, I’d go with Crosby Stills and Nash.
Tiny Tim?
To me great voice and great singer are only marginally related.
The three who came to mind when I saw this thread:
Sam Cooke
Tom Waits
Colin Blunstone (the Zombies). Every time I listen to Odyssey and Oracle, which is still often, I’m simply blown away by his singing. I wish he recorded more.
Gordon Lightfoot
Robert Plant (Led Zeppelin)
Jon Anderson (Yes)
Ian Anderson (Jethro Tull)
John Kay (Steppenwolf)
Dan Hartman (Edgar Winter Group)
Lennon, McCartney, Harrison (Beatles)
djm
And in ITM:
Sean 'ac Dhonncha
Darach Ó Catháin
Dhiarmuid O Suilleabháin
djm
Enrico Caruso (tenor) listen
John McCormack (Irish tenor)listen
Jussi Bjorling (tenor)listen
Luciano Pavarotti (tenor)listen
You’re breaking Cowtime’s rules here Doug, but I like your choices.
I must confess to minor ADD (attention deficit disorder) in that I often overlook instructions, and I can’t remember what else that I was going to say here. Oh, yes! I was going to second Paul Robeson. I wish that I could have heard one of his live concerts. His booming bass voice is in sharp contrast to the four tenors mentioned previously.
Tom Waits
Fher Olivera
James LaBrie
As with the other thread, I can’t believe I missed him. I’d also say that I think he’s one of the most underrated rock singers – Listen to Don’t Step on the Grass Sam and Snowblind Friend back-to-back. It’s hard to believe it’s the same guy.
Josh Groban (He has the voice of a god.)
After him, I’d have to go with:
Frank Sinatra
Josh Turner (What a bass!)
John Mayer
Cole Porter
Peter Gabriel– I was just telling my husband the other day (we were listening to PG in the car) that Gabriel could be singing the phone book and I would still be drawn in!
Iarla O Lionaird– before he was vocalist for Afro Celt, he was a sean nos singer. He can take a breath and sing an agile, ornamented phrase that lasts about a minute and a half. Makes it seem effortless. 
He has 2 solo albums out that are experimental music, some of which is kinda-sorta OK and some of which is heart-piercing.
Nobody’s mentioned Bono?