Cover songs that are better than the originals.

Two by Ben Folds:
Common People (original by Pulp) on William Shatner's "Has Been" Album
Bitches Ain't Shit (original by Dr. Dre) from "supersunnyspeedgraphic, the lp"

NRBQ's cover of Johnny Cash's "Get Rythm" - so good that Johnny started to play it like them after hearing it

Kat Edmonson's version of Brian Wilson's "I Just Wasn't Made for These Times" is not necessarily better than the Beach Boys' original but it is great in its own way.

John Prine's cover of Blaze Foley's "Clay Pigeons" from "Fair & Square"

Glen Campbell's cover of Paul Westerberg's "Ghost On the Canvas" (Paul's recording is almost unlistenable - Glen's is genius).

There's been many mentions of "Sweet Jane". My vote is for Mott The Hoople's version.

Did anyone mention Molly Hatchets cover of "Dreams"by the Allman Brothers Band?

Did anyone mention Molly Hatchets cover of "Dreams" by The Allmans Brothers Band