I think the Bauhaus cover of “Ziggy Stardust” surpasses the original.
Thinking of Bowie covers, I like Beck’s “Diamond Dogs” better than the original. He managed to leave out the silliest lyrics, too.
Thinking of songs from the Moulin Rouge soundtrack, I kinda like the version of “Your Song” performed by Ewan McGregor and Alessandro Safina, but I don’t care for the original Elton John song at all.
Pearl Jam’s cover of “Last Kiss” was an improvement on the earlier three versions, but that’s not saying a whole lot…there’s only so good any version of that song could be.
“I Fought the Law” by the Crickets was far surpassed by the Clash’s version.
“Baker Street,” orig. by Gerry Rafferty, was tremendously improved by the Foo Fighters. First and foremost by getting rid of those awful flute and sax bits.
Come to think of it, The Clash’s cover of “Brand New Cadillac” was far better than the original as well. I can’t recall who first did the song.
Many more, but those are off the top of my head. Oh! Who did that cover of “Jet Plane,” the Mamas & Papas song? It was a woman; can’t remember her name, but that was great.
John Denver wrote it, but, afaik, The Mamas & The Papas never covered it. The one that gets played most often is done by Peter, Paul & Mary. Don’t know which cover you’re thinking of, with the woman.
Hendrix did the essential performance of “Like a Rolling Stone” at Monterey Pop, blowing away Bob Dylan and all other subsequent attempted versions. “Excuse me a minute, just let me play my guitar” indeed!
More recently and more trivially…somebody or other in the pop music circuit just recently redid “When I Fall in Love”, which I first heard as an annoying tune by a 60s group called The Lettermen. The new version is much better, not that I care enough to find out who they are.
Marvin Gaye’s cover of I Heard It Through the Grapevine, which also spent seven weeks at #1, released a year after Gladys Knight had a big hit (#2) with it–and vastly superior.