There are a lot of good covers out there but most dont quite live up to the original, here is a short list of covers that are on par or even better than the original:
Jimi Hendrix cover of Bob Dylan "All Along the Watchtower"
-Jimi took ownership of this song
Richie Havens cover of the Beatles "Here Comes the Sun"
-cool variation, Richie Havens sounds like a dozen acoustic guitar players at once
Sarah McLachlan cover of XTC "Dear God"
-adds emotion
Johnny Cash cover of Nine Inch Nails "Hurt"
-Johhny lives and breathes "Hurt" in his twilight years
Stevie Wonder cover of the Beatles "We Can Work It Out" -funky
Joe Cocker cover of the Beatles "With a Little Help From My Friends"
-made it a generationl anthem
Janis Joplin cover of Kris Kristofferson "Me And Bobby McGee"
-Its hard to imagine anyone but Janis Joplin singing this.
Here are some covers which are complete crap compared to the original:
Perfect Circle Covering John Lennon "Imagine"
-They sucked the hopeful aspect of the song and replaced it with vileness
Disturbed covering Genesis "Land of Confusion"
their attempt to make it sound more heavy and edgy feels phoney to me