In memory of John Stewart (“Gold” with backup singer Stevie Nicks)
My daughter and I were listing some of these songs the other night, and I thought it would make an interesting thread, so here it is.
A few examples to start the ball rolling:
Games Without Frontiers (Kate Bush)
Bad Blood (Elton John)
Money For Nothing (Sting)
Aaliyah sang behind Notorious BIG on “One More Chance.”
You’re so Vain (Mick Jagger)
Walk Away Renee (Steven Tyler)
How about some 80s? 
Rockwell (1980s two hit wonder with “Someone’s Watching Me” and “Obscene Phone Caller”) has Michael Jackson singing backup on both songs.
Stevie Wonder’s 1980s hit “Part Time Love” had Luther Vandross on backup.
Glass Tiger’s one hit “Don’t Forget Me When I’m Gone” featured Bryan Adams showing some Canadian solidarity.
As did Rush’s “Time Stand Still,” featuring Aimee Mann of 'Til Tuesday.
Most or all of the Eagles played and sang on Randy Newman’s album Little Criminals, which included his hit Short People.
He does sing a verse himself in one version, but Tyler backed up Pink on “Misery.”
“Galileo” by the Indigo Girls features Jackson Browne on backing vocals.
Their song “Kid Fears” features Michael Stipe, but he’s more prominent than backup vocals.
Katey Sagal (best known as Kate Bundy and the voice of Leela on Futurama) started as a backup singer, for Bette Midler and others:
John Lennon sang backup on Elton John’s version of “Lucy in the Sky with Diamonds.”
Neil Young’s “Heart of Gold” had Linda Ronstadt on backing vocals.
Phil Collins sings backup on the Eric Clapton song “Bad Love” (and is also the drummer), and also sings backup on the David Crosby song “Hero.”
Ronnie Spector famously added vocals to Eddie Money’s Take Me Home Tonight.
How’s 'bout David Crosby showing up on Hold My Hand by Hootie and the Blowfish.
Magnet & Steel- Stevie Nicks
Sentimental Lady- Christine McVie
I wouldn’t consider her a backup singer, but Ellen Foley sang the female vocals on Meatloaf’s “Paradise By The Dashboard Light.” She went on to later, greater (?) fame as the public defender in the first few seasons of “Night Court”.
Lou Rawls can easily be heard in Sam Cooke’s “Bring it on Home to Me.”
Linda Ronstadt backs up Nitty Gritty Dirt Band in “American Dream.”
The Big Bopper on Johnny Preston’s “Running Bear”, which he also wrote.
On “If I had a Million Dollars” by Barenaked Ladies, there are back-up vocals sung by several Canadian musicians and friends of the band including Moxy Fruvous, and Rheostatics.
Blind Melon’s Shannon Hoon was a strange choice to sing back-up on the Guns & Roses hit “Don’t You Cry.”
I suppose we could debate the famous-ness of Hoon, but there ya go.
Olivia Newton John backed John Denver on “Fly Away.”
And James Taylor, IIRC.
Jimmy Buffett, among others, sang backup of the Eagles’ “The Greeks Don’t Want No Freaks.”