Cover Songs that are better than the Original


Eva Cassidy - Fields of Gold
Eva Cassidy - Over the Rainbow
Eva Cassidy - True Colors
Eva Cassidy - Time after Time
Eva Cassidy - Autumn Leaves
Johnny Cash - Hurt
The Who- Rush cover - The Seeker
Rush cover -The Pass  Fleesh Version

klimt
Agree with you on People Get Ready; might not be better than the original (at least the vocal side, not a big fan of Stewart's voice), but the guitar work by Beck is superb.
Money (That's What I Want) Flying Lizards in 1979
 covered by the Beatles in 1963
 written by Berry Gordy and Janie Bradford,
   performed by Barrett Strong 1959
Mr Tambourine Man covered by the Byrds 1965
 Bob Dylan also 1965