Some really great suggestions that I hadn’t thought of.
Didn’t Nancy Sinatra and LeeHazelwood do some other duets
Summer Wine was one I think
Michael Buble and Nelly Furtado’s Quando Quando Quando is unexpectedly nice.
Gram Parson Emmylou Harris: Love Hurts
(A lot of good ones in this thread I might add)
Oo, I will. I love her and Don Henley on “Leather and Lace”.
Emmylou Harris and Dave Matthews on “My Antonia.”
James Ingram and Patti Austin on “Baby Come to Me.”
Garth Brooks and Trisha Yearwood “In Another’s Eyes” and “Wild as the Wind”
Emmylou Harris and John Denver “Wild Montana Skies”
Or “Don’t Give Up”
Rick James & Teena Marie: Fire & Desire
Linda Ronstadt and Aaron Neville, “Don’t Know Much” and “All My Life”
Peter Cetera and Cher, “After All”
Peter Cetera and Amy Grant, “Next Time I Fall in Love”
Dan Hill and Vonda Shepherd, “Can’t We Try”
Ann Wilson and Mike Reno, “Almost Paradise”
Whitney Houston and Jermaine Jackson, “If You Say My Eyes Are Beautiful”
Phil Collins & Frida (of ABBA)–Here We’ll Stay
Forgot to add:
Vanessa Williams and Brian McKnight, “Love Is”
Peabo Bryson and Celine Dion, “Beauty and the Beast”
Joni Mitchell and James Taylor - Close Your Eyes
Rickie Lee Jones and Dr. John - Makin’ Whooppee
Jonatha Brooke and Neil Finn - New Dress
Shawn Colvin and Neil Finn - What I Get Paid For
I like Neil Finn.
Linda Ronstadt and James Ingram - Somewhere Out There
Phil Collins and Marilyn Martin - Separate Lives
Whitney Houston and Teddy Pendergrass - Hold Me
Meat Loaf and Cher - Dead Ringer for Love
Peabo Bryson and Regina Bell - A Whole New World (Aladdin)
I’m the first the mention?
Kenny Rogers and Dolly Parton - Islands in the Stream
There’s a new Gretchen Wilson/John Rich duet titled “Come to Bed”. Yummy.
Very different from most of the choices in this thread: “Same Time Next Week,” vocals by John Wetton and Doreen Chanter, from Phil Manzanera’s Diamond Head album. In another forum I once described this song:
You know, I listened to that song yesterday, and I thought of it, but it really isn’t that good a song. In my opinion, of course. 
Jim suggested k.d. lang and Roy Orbison - “Crying”
I just listened to Kenny Rogers and Sheena Easton’s “We’ve Got Tonight,” and holy crap , do they sing the hell out of that song. They should make all American Idol hopefuls listen that song and learn about touch and crescendo and full-out singing without oversinging.