The Righteous Brothers, of course. Proof that in the best duos, the voices need to complement each other - between them, they cover virtually the entire range of audible sound.
Of course, identical voicesalso works.
:smack:
Huge Wham! fan and didn’t even think of that! Ditto Smos Bros.
Great list.
I saw her at the Sydney Opera House a couple of days ago in The Songs of Nick Drake. Awesome.
Pet Shop Boys
Tears for Fears
Erasure
Yazoo
Soft Cell
um, Jedward?
And who could forget Glenn & Chris (Hoddle and Waddle)? (Could they contact me with advice as to how I might forget too?)
Egads. I’ve actually MET Pet Shop Boys multiple times (favorite. act. evar.) and didn’t even think of them. D’oh!
Flat and Scruggs
Sugarland
Loretta Lynn and Conway Twitty
John Prine and Iris DeMent
I really like country music.
Not exactly what you asked for, but both Frank Sinatra and B.B. King have albums of duets with various partners. And one of my all-time favorite duet songs is Dean Martin and some chick doing “Baby It’s Cold Outside.”
If jazz is your thing Jackie and Roy did some good stuff. Check out some of their work at Jackie & Roy - Don’t Be Blue and nearby clips.
Jan & Dean
Carly Simon & James Taylor
The Carpenters.
Piano/Hammond and guitar work well as a duo format – keys can cover the bass, and basically style of music will work. George Jones ballads, honky-tonk, straight-ahead jazz, funk, rock and roll, rhythm and blues. I can’t think of any piece of music that wouldn’t work, especially if the musicians are good at getting the right sounds and know how to play.
I have a feeling you’re thinking more about pop music with vocals, though, but nothing’s precluded as long as someone can/wants to sing in the duo.
Flipping through my very dusty cassette tape collection: Eurhythmics, Roxette, OMD, and erm… Air Supply.
Also:
Oh yeah… Speaking of the 80s, there’s also Naked Eyes.
Somewhat more recently, Fleming & John.
Garfunkel and Oates, anyone?
I’m loving all these suggestions; thanks a lot, everyone!
Actually, literally anything goes, definitely not just pop music. The background - my wife was a professional musician (singer, and rhythm guitar) before university cut down on her time for gigs. I’ve been an amateur musician all my life (mainly brass and woodwinds, but also electric bass and mandolin). We are - again - floating the idea of playing together, hopefully with regular gigs, and I want to see what’s been done in the past, and what we could do well together. However, I fear I’ll have to learn to play her spare guitar to really fill up the melodic counterpoint and harmony; we’ve already tried playing together with guitar&flute and guitar&mandolin, and it just sounds too thin. This thread is for inspiration and ideas 
Brooks & Dunn
62 West
and how about Johnny & June Carter Cash? Would they count as a duo?
In R&B:
Marvin Gaye & Tammi Terell
Ashford & Simpson
In classic rock:
Loggins & Messina
David Crosby & Graham Nash (released a few records in the mid-70s w/o Stills or Young)
In alternative:
Indigo Girls
Shakespeare’s Sister
Throwing Muses (the last album at any rate was just Kirsten Hirsch and one guy.)
Let me second Gillian Welch (w/David Rawlings), if you’re into the country end of alt-country.
And, if we’re in alt-country, and not limited to particular established bands/groups, then I’ll add to the list of great duos:
Willie Nelson with anybody (you’d think the ability to hold a pure note would be a prerequisite for being a good dueter, but somehow being the opposite of David Rawlings works, too); and
EmmyLou Harris with nearly anybody. She really gets around, and usually improves things when she does.
And Ween, back when they were just Gene & Dean.