Apart from the very obvious ones (Roy Orbison, Elvis Presley, Van Morrison, etc…) I would add Antony Hegarty. Seriously one of the most beautiful and moving voices I’ve heard over the years.
Not terribly well-known in Europe or the US but fantastically popular in India: The sisters Lata Mangeshkarand Asha Bhosle have absolutely beautiful voices - and they have been put to good use. A rather conservative estimate is that they have recorded around 20.000 songs between them! Wonderful voices!
One of my favorite Lata Mangeshkar songs: Dil to hai dil.
No Liz Fraser? Brendan Perry gets a look in, but not ex-bandmate Lisa Gerrard?
A lot of my favourites have been mentioned. Patsy Cline, Karen Carpenter and Elizabeth Fraser very high up my list.
But two not mentioned yet I don’t think
Briana Corrigan (ex- beautiful south)
Harriet Wheeler (The Sundays)
I’ll see your Mariah Carey and raise you Yma Sumac. The woman not only had a five-plus octave range (from baritone to bats, basically) but she could do some seriously inhuman things with it. Here’s a bit of musical weirdness that shows off both the range and some of the effects. Unearthly. She’s like Bjork to the power of ten.
Personally, though, I prefer her better-known mambo Gopher. No, I don’t know why it’s called that.
Doesn’t get much better than Maddie Prior.
Weird, but a good weird.
The comparison with Bjork is a good one. they have more than just vocal gymnastics in common. There is also a certain, strangeness. Can’t put my finger on it but it is definitely there.
Ha! I heard Yma Sumac on my fav internet radio station Radio Paradise, and looked her up. I read about the five octave range and then read that the only modern popular artist to rival that was…the unlikely star Mariah Carey. Which was weird because Carey’s stage image is much more that of a sexy kitten than that of a serious vocal artist.
Another modern voice artist is the Dutch performer Greetje Bijma. Originally an award winning jazz singer, she is the modern Yma Sumac and prefers to do really weid things with her voice, when just pretty singing becomes too boring. Look her up on Youtube.
Liz Fraser ex Cocteau twin (as mentioned previously).
Annie Haslam from Renaissance.
One that I rediscovered this week is Julie Covington. See her on this version of In My Life:
http://www.youtube.com/watch?v=8oZS0tP0oP0
Soulmurk, we are soul mates.
Dudu Fisher. Went from synagogue cantor wto playing Lonfon Les Miz’s Jean Valjean in one audition.
I’ll second Freddie Mercury.
And add Nicole Atkins to the list.
Some really great ones mentioned, I’ll only add:
Tori Amos
Vince Gill
Great minds, and all… just don’t tell my wife 
Another one that occurs to me but that also might push the definition of “popular” is Beth Gibbons of Portishead.
Not mentioned yet is the man with the most perfect tenor pop voice I’ve heard in years - Raul Malo. He was formerly with the alt-country band the Mavericks, now solo. Think Roy Orbison
Here is one of my favorites, a love song to tolerance “Matter Much To You”.
(Hello all. Long-time lurker, first-time poster.)
For me, there’s only one answer: Bing Crosby. His voice is like velvet and listening to some of his songs makes me melt.
I second Bing Crosby and nominate Simon LeBon of Duran Duran fame. They share an ability to take an okay or even firmly mediocre song, and own it and make it shine.
No mention of Dido yet?
In the “haunting but beautiful” category, let me nominate Geoff Tate of Queensryche. Here’s a clip of him doing the national anthem. And this is him singing a cover of Simon and Garfunkle’s “Scarborough Fair.”
We’ve seen Simon LeBon (with Duran Duran) and David Bowie live fairly recently, and they have both impressed us with their vocal abilities.
As for five octave vocal ranges, I didn’t want to nominate Prince for the most beautiful/perfect voice because while his is extremely nice and versatile, he isn’t, in my opinion, the most perfect singer, but his range rivals Mariah Carey’s. He sings very nicely and perfectly in control way, way down low and way, way up high.