Swim Until You Can't See Land covered by Benjamin Francis Leftwich. So much nicer than the original by Frightened Rabbit

Girls just want to have fun by the maine

All along the Watchtower by Hendrix. Dylan is great but Hendrix version is even better if thats possible

Add me to the list of people who prefer Stevie Ray Vaughan's versions of Hendrix tunes over the Hendrix originals. Not that Hendrix wasn't great, but somehow, SRV's takes seem to make more sense.

The Clash - Police and Thieves and Wrong Em Boyo (But I prefer most of their cover versions to the original versions)
Soft Cell - Tainted Love
Happy Mondays - Step On

Joe Cocker, "With a Little Help from My Friends"
Joe Cocker, "The Letter"
Joe Cocker, "Cry Me a River"
Hendrix, "Like a Rolling Stone"
Hendrix, "All Along the Watch Tower"
Brian Setzer, "Sleepwalk"
Los Lobos, "La Bamba"
Ozzy's entire cover of his Black Sabbath songs on the Speak of the Devil album beat out many versions of the originals and I love Black Sabbath.
Alice Cooper "Hello, Hooray!"
Watson Twins "Just Like Heaven"

Let's dance - the ramones cover.

The man who sold the world - nirvana cover

Most originals are better than the covers :p