Bluesman Jaybird Coleman cut an (alas) unreleased He May Be My Last Time, I Don't Know for Gennett around '27.
Five Blind Boys Of Alabama [as This May Be The Last Time]
Alex Bradford [idem]
Staple Singers [idem; with Mavis Staples; may be the source for the Stones version]
James Brown [as Maybe The Last Time]
Rolling Stones [n°1 UK as The Last Time; 'I have no idea where Keith or Mick heard the song; it's not the sort of thing that got played on the radio' - Bill Wyman in his Blues Odyssey (DK); their intro was inspired by King Curtis' instrumental Beach Party]
Ronnie Bird [as Elle m'attend]
Who [minus John Entwistle to support Jagger & Richards on the verge of being send to prison]
Paul Black & The Flip Kings [as The Last Time]
Mike Henderson [idem]
Dwight Yoakam [idem]
Black Dub [a Daniel Lanois production with Trixie Whitley]
Wynton Marsalis [with the Blind Boys Of Alabama]
The signature Jagger/Richards doesn't always make it a Stones record. This one belongs to the Lord himself. For the Bitter Sweet Symphony connection, see: The Last Time.