Song covers that are better than the originals

Dance Society"s cover of the Stones "1000 Light Years From
Home"

The Cure's cover of "Purple Haze" on the Hendrix tribute album "Stonefree"

Johnny Cash - Hurt. Way WAY better. One of the seminal recordings of the decade.

other honorable mentions - with a jazzy bent:

Bjork's Hyperballad - covered by that polish piano guy on ECM that I can't pronounce.

Pat Metheny and Charlie Haden - "Moon is a Harsh Mistress" is amazing. Dozens of guys trying to play it on youtube - doing covers of his cover if you will. Jimmy Webb's own recent recording is pretty nice.

Bill Frisell doing Madonna's Live to Tell or John Hiatt's Have a Little Faith... OK, hard to say they are "better" but for a jazz fan "more interesting."

Jeff Beck's A Day in the Life. I know you can't beat the beatles, but his is better than Paul McCartney's recent live version if you ask me.

I like Elliot Smith doing SuperSonic better than Oasis.

And lastly -rap anthem Straight Outta Compton, NGA original. Nina Gordon's delicate ACOUSTIC version is incredible, melodious and hilarious.

agree with gdoodle on johnny cash. personally, i think the seeemingly endless series of his "american recordings" covers albums are way overhyped, but "hurt" is the song he was born to sing.
i don't know if anyone's mentioned the ultimate cover band, this mortal coil, who absolutely nail some fantastic, if underheard songs like "i am the cosmos" (chris bell), "strength of strings" (gene clark) and "another day" (roy harper), which is arguably the prettiest song in the english language.

Clapton's cover of J.J. Cale's "After Midnight"

Jimi Hendrix version of Dylans "All Along the Watchtower"