Song covers that are better than the originals

R.E.M.'s covers of "Wichita Lineman" and "Galveston". Sadly, the latter is only available on YouTube as a snippet. While I prefer John Hartford's rendition of "Gentle on My Mind", R.E.M.'s version is much better than Glen Campbell's. Michael Stipe is a big fan of Jimmy Webb and John Hartford and R.E.M. has covered Webb in concert; I wish more of those were available on CD/vinyl.
The Doors' cover of Kurt Weill's "Alabama Song".
Gary Jules' version of "Mad World".

Devo's Jumping Jack Flash

Hendrix "All Along The Watchtower" by a mile. Even Dylan changed his way of performing it after Jimi.
Jeff Buckley doing Leonard Cohen's "Hallelujah," is another winner.

Golden Palominos covering The Ocean by Led Zeppelin. Don't think they ever recorded it, but they performed it as the encore at the Paradise in Boston on 3/7/86. Syd Straw on lead vocals, with Jack Bruce and Bernie Worrell in the band. Awesome show, awesome cover.

David

Mary J Blige's rendition of U2's "One".