Duets I know and would like to do:

Mockingbird by Carly Simon and James Taylor
The Monster by Rihanna and Eminem
Stumblin' In by Suzi Quatro and Chris Norman
Reunited by Peaches and Herb
Guilty by Barbra Streisand and Barry Gibb
All My Life by Linda Ronstadt and Aaron Neville
You and I by Crystal Gayle and Eddie Rabbitt
Islands in the Stream by Dolly Parton and Kenny Rogers
You're the One That I want from Grease
Somewhere Out There by Linda Ronstadt and James Ingram
Don't Know Much by Linda Ronstadt and Aaron Neville
Almost Paradise by Ann Reno and Mike Wilson
Whenever I Call You Friend by Kenny Loggins and Stevie Nicks
Where Is the Love by Roberta Flack and Donny Hathaway
The Closer I Get To You by Roberta Flack with Donny Hathaway
Stop Draggin' My Heart Around by Stevie Nicks With Tom Petty And The Heartbreakers
You Don't Have To Be A Star (To Be In My Show) by Marilyn McCoo & Billy Davis, Jr.
Too Much, Too Little, Too Late by Johnny Mathis & Deniece Williams
Leather and Lace by Stevie Nicks and Don Henley
Up Where We Belong by Joe Cocker and Jennifer Warnes

Already recorded these before online but I can do them again if need be:

A Whole New World (from Aladdin)
Ain't No Mountain High Enough by Marvin Gaye and Tami Terrell
All I Ask of You (from Phantom)
Beat Goes On by Sonny and Cher
Dammit Janet (from Rocky Horror Picture Show)
Don't Go Breakin' My Heart by Elton John and Kiki Dee
Endless Love by Diana Ross and Lionel Ritchie
Everything's All Right (from Jesus Chris Superstar)
Over at the Frankenstein Place (kind of a group song but we split up the male parts or even see if others want to join - from RHPS)
People Will Say We're in Love (from Oklahoma)
Time Warp (also group song from RHPS)
Sue Me (from Guys and Dolls)
Tonight (from West Side Story)
Tonight I Celebrate My Love for You by Robert Flack and Peabo Bryson
Unforgettable by Nat King Cole and Natalie Cole
We've Got Tonight by Kenny Rogers and Sheena Easton
With You I'm Born Again by Billy Preston and Syreeta
You Don't Bring Me Flowers by Neil Diamond and Barbra Streisand
 

Showtunes:

All Er Nuthin' (from Oklahoma)
All Through the Night (from Anything Goes)
Anything You Can Do (from Annie Get Your Gun)
Do You Love Me? (from Fiddler on the Roof)
Goodnight & Thank You (from Evita)
High Flying, Adored (from Evita)
I Have Dreamed (from King & I)
I'd Be Surprisingly Good For You (from Evita)
I'd Do Anything (group song from Oliver)
If I Loved You (from Carousel)
I'll Know (from Guys and Dolls)
I've Never Been in Love Before (from Guys and Dolls)
It Only Takes A Moment (from Hello Dolly)
It's De-Lovely (from Anything Goes)
Lida Rose (sort of a group song but could be a duet - from Music Man)
Make Believe (from Showboat)
Now I Have Everything (from Fiddler on the Roof)
Rain in Spain, The (group song from My Fair Lady)
Rainbow Tour (from Evita)
Show Me (there's only a little bit of the guy- from My Fair Lady)
Sixteen Going on Seventeen (From Sound of Music)
Sunrise Sunset (from Fiddler on the Roof)
Think of Me (from Phantom of the Opera) only sort of a duet)
Till There Was You (only a small part is the man's - from Music Man)
Waltz for Evita and Che (from Evita)
We Kiss in a Shadow (from King & I)
What do the Simple Folk Do (from Camelot)
You're the Top (from Anything Goes)
 

Other songs I know and like less:

Baby It's Cold Outside
Brady Bunch Theme
Family Ties theme by Deniece Williams and Johnny Mathis
I Got You Babe by Sonny and Cher
Love Shack by the B52's
Say Say Say by Michael Jackson and Paul McCartney
Somethin' Stupid Frank Sinatra and Nancy Sinatra
Summer Nights (from Grease)
That's What Friends Are For (group song) by Dionne Warwick, Elton John, Gladys Knight and Stevie Wonder.
Three's Company Theme by Ray Charles & Julia Rinker
What Kind of Fool (Barry Gibb and Barbra Streisand)
Why do I Love You? (from Showboat)
You Are Love (from Showboat - my favorite actually!)


I have these but don't know them well, probably not too hard to learn

Ain't Nothing Like the Real Thing by Marvin Gaye and Tami Terrell
Baby Come to Me by Patti Austin and James Ingram
Beauty and the Beast by Celine Dion and Peabo Bryson
Cruisin' by Huey Lewis and Gwyneth Paltrow
Quando Quando Quando by Michael Bublé and Nelly Furtado
 

If it's not on this list, I may not know it, but if it's easy to learn, I'm game!