Excluding Gimme Shelter of course.
All jokes regarding her vocal ability aside, I’m a huge fan of Linda McCartney’s on “Silly Love Songs”, as well as Stevie Nicks on John Stewarts “Gold” and whoever did the ones on Bob Segers “Still the Same”.
Clare Torry on “The Great Gig In The Sky” from Pink Floyd’s Dark Side of the Moon (although I don’t know if what makes her stand out could really be called “background” vocals.)
The choir on “I Want To Know What Love Is” by Foreigner.
Kate Bush on Peter Gabriel’s “In Your Eyes”. (Or Paula Cole on the live version from Secret World Live.)
Sandy Denny on Led Zeppelin’s “The Battle Of Evermore”.
just off the top of my head
The entirety of Paul Simon’s Graceland.
The choir on Joe Cocker’s “With a Little Help from My Friends.”
Pete Townsend’s backing vocals on many Who songs, but especially “Summertime Blues.”