Say, Say, Say by Paul McCartney and Michael Jackson.
The Highwayman, which Sampiro mentioned, is performed by Johnny Cash, Willie Nelson, Waylong Jennings and Kris Kristofferson.
And how 'bout the catalog of Simon & Garfunkel?
Check out the country “Brother Acts”.
Bill & Charlie Monroe sang together before Bill went off to start his band. Ralph & Carter Stanley were also bluegrass pioneers. The Delmore Brothers were a bit bluesier & the a recent tribute album honors the Louvin Brothers. Genetically similar voices & lifelong experience singing together make for real “goosebump” harmonies. Look for anything by these duets.
The Everly Brothers brought this mountain tradition into modern times. Nick Lowe & Dave Edmunds devoted an EP to Everly duets.
The Bernal brothers made some hits here in Texas, back in the 50’s. Their “Mi Único Camino”–featured in the soundtrack of Lone Star–showed some “goosebump” harmonies in Spanish. Then, there are the classic Mexican trio acts…
[ul]
[li]Baby Grand, Billy Joel & Ray Charles (it’s not on the album that SuperNelson mentioned)[/li][li]Peace on Earth/Little Drummer Boy, Bing Crosby & David Bowie[/li][/ul]
Sampiro’s right. Angel’s referred to as both “he” and “she” in the script. Collins usually calls him “he”, whereas Maureen and Mimi call her “her.” Make of that what you will.
'Sides, voices is voices, and the song’s definitely written for a tenor, not an alto. 
The magnetic fields - “the one you really love”
TV on the radio - “dreams”
the Human League - “keep feeling fascination”
On Johnny Cash’s last album (American IV), he does a duet of “Desperado” with Don Henley, and “I’m So Lonesome I Could Cry” with Nick Cave.
Nick Cave and the Bad Seeds : The Weeping Song
- another “father and son” song, but Cat Stevens it is not.
You should hear Where the Wild Roses Grow, with Blixa Bargeld in the female role. Very strange.
And of course, though both have recorded it separately, the canonical version of “Don’t Let the Sun Go Down on Me,” which Elton John wrote for George Michael, is the concert version that they perform together.
This CD by Ray Charles is all duets, and it include ones with James Taylor, Elton John, Willie Nelson, Michael Mcdonald, B.B. King, Johnny Mathis, and Van Morrison.
*There’s nothing better than love * by Luther Vandross & Gregory Hines
Gerald Lavert and his father did a whole album of duets most notably “Apples Don’t Fall”
I now have “All For the Best” stuck in my head, never mind that I haven’t heard it in years. Thanks, moriah and Liberal! 
Gilbert and Sullivan operettas have plenty of duets for male singers –
“Kind Captain, I’ve important information,” HMS Pinafore (baritone/bass)
“When I go out of door,” Patience (two baritones) – this one’s fun
“You understand? I think I do,” Ruddigore (tenor/baritone)
“Hereupon we’re both agreed,” Yeomen of the Guard (two baritones)
“We’re called gondolieri,” The Gondoliers (tenor/baritone)
“In every mental lore,” Utopia Limited (two baritones)
Can’t think of any others offhand that aren’t part of a larger musical number and don’t have chorus backing, but I’m sure there are more…
I’d echo the Simon and Garfunkel recommendation. Depends what you’re looking for of course, but they’ve got a fair amount of breadth to choose from.
Polycarp, not quite sure what you’re saying here, but if it’s that Elton John wrote “Don’t Let the Sun Go Down on Me” for George Michael, he didn’t. Its copyright date is 1974 with the lyrics written by Bernie Taupin. If you’re saying that there was an updated version a la “Candle in the Wind” I didn’t realize that. My favourite version of the song is the “live” version done in concert in the 80s. I still like the song even if it did take me…cough…years to realize that the line “I can’t light no more of your darkness” wasn’t really “I can’t light no more Augie Dog days”. What can I say, too many cartoons as a child.
“How Come, How Long” - Kenneth “Babyface” Edmonds & Stevie Wonder
“No More” Into the Woods
Robbie Williams does a couple male/male duets on his album Swing When You’re Winning: Well Did You E’vah? with Jon Lovitz, They Can’t Take That Away From Me with Rupert Everett and They are surprisingly good.
The Immortal Louis Armstrong and the Great Bing Crosby did a sly little humorous number called Gone Fishin’.
Shangri-La! 
[QUOTE=Katisha]
I now have “All For the Best” stuck in my head, never mind that I haven’t heard it in years. Thanks, moriah and Liberal!
You’re welcome.
Here, let me put this into your head: Have you ever seen the TV Movie trainwreck known as “Steven King’s ‘The Langoliers’”?
Now, imagine the song, “We’re the Langolieri”
Pleasant dreams.
Peace.
“Agony” is better.
The Stylistics: “You Make Me Feel Brand New”.