I’ve always loved “They Don’t Know” by Tracey Ullman, but only recently discovered that (A) it was previously a single by Kirsty McColl, and (B) McColl actually sang backup on Tracey’s slightly later version (Both singers were under contract with Stiff Records at the time). This probably happens a lot, like Steven Tyler on Run-DMC’s cover of “Walk This Way,” but are there many other instances?
–Mick Jagger was in the video for Bette Midler’s “Beast of Burden,” I forget if he sang
–Johnny Cash and Ronnie Spector guested on songs that were kind of about their older hits, by Rodney Crowell and Eddie Money, respectively
–Sippie Wallace guested on Bonnie Raitt’s cover of “Woman Be Wise”
The Fat Boys did a version of The Twist featuring Chubby Checker. Chubby did perhaps the most famous previous version of the song although not the original.
British Boy Band Five released a version of Queen’s We Will Rock You in the year 2000 featuring the, by then, only two active members of the original Queen: Brian May on guitar and Roger Taylor on drums.
The song which became Shipbuilding had a vaguely complicated history but the final lyrics are credited to Elvis Costello. The most famous version of the song is by Robert Wyatt and has Costello on backing vocals.
Kirsty MacColl did a cover version of the Billy Bragg song A New England. Although he didn’t play on the new version he did write an extra verse for Kirsty since the existing song was too short.
Carl Wilson sang backup on David Lee Roth’s version of “California Girls.”
Kerry Livgren appears on a version of “Carry On Wayward Son” by an all-female group called Rachel Rachel. (I’m not sure whether he plays on the track or just appears in the video.)
The song Living Doll was a hit for Cliff Richard and the Shadows in 1959 (according to Wikipedia the Shadows were known as the Drifters at the time.) It was re-recorded as a very successful charity single by the anarchic comedy team The Young Ones (perhaps best known for their Eponymous TV show) in 1986. Cliff did the vocals and guitarist Hank Marvin of The Shadows also joined Cliff for the first time in over a decade.
Gene Pitney recorded a reasonably successful version of Something’s Gotten Hold Of My Heart in 1967. Marc Almond (best known for being half of Soft Cell) did a version in 1988 which Pitney heard and liked so much he recorded it as a duet with Almond and that version became a UK hit in 1989.
Maybe not 100% of what the OP is looking for, but Emmylou Harris sang duet and backing vocals on several recordings on the Gram Parsons tribute album “Return Of The Grievous Angel”, songs on which she had dueted with Gram Parsons on the original recordings, for instance:
On Kelly Clarkson’s debut album, Danielle Brisebois provide backing vocals on a cover of her own song “Just Missed the Train”. I love the song and love Danielle.