Pulp, "Common People". Named the greatest Britpop song of all time by Rolling Stone. Later covered by William Shatner.
2Pac, "California Love". Joe Cocker also knows how to party. No one covered this that I know of, although since there are at least 7 2Pac versions, covers aren't really needed.
Bruce Springsteen, "The Ghost of Tom Joad". To an extent, this video represents Bruce covering himself. The original was mostly acoustic. Later it was covered by Rage Against the Machine. Finally, Rage guitarist Tom Morello joined Bruce and the E Street Band for this version, which to my mind is easily the best.
Coolio, "Gangsta's Paradise". This is something of a cover version itself, given how heavily it samples Stevie Wonder's "Pastime Paradise". Wonder even gets a songwriting credit. According to the inescapable Wikipedia, there are no profanities, because Wonder wouldn't have it.
Jewel, "Who Will Save Your Soul". At last, my cover version conceit is defeated ... I don't think anyone ever covered this. So I'm left with this anecdote: in 1995, I saw Jewel open for the next act on this list.