A good cover of a song usually finds something new in an original song. Everyone and their mom seemed to cover Radiohead, and often with good results...
Paranoid Android - UMASS Drum Line: gorgeous instrumental
Just - Mark Ronson: Funked up beauty
Radiodread - Reggae covers, I especially like "Karma Police"
and Hard N Phirm's ''Rodeohead" - Blue-grass medley, funny! Audio hosted by a fan, strange interface, worth the listen.
Long ago I grabbed the "Skeet Spirit: The Krunk Tribute to Radiohead" and now it's nowhere to be found. Worth hunting.
A greatly bad cover is all the better in my book. Rod Stewart's "Do You Think I'm Sexy" took a hit from the Revolting Cocks and Those Damn Accordions. Accordian make everything better from The Dead Kennedys (Duckmandu) to Pink Floyd (Polka Floyd).
Copy, Right? has been favorite of mine for introducing me to covers I never would have heard. Most recently found on that site the Monsieur Blumenberg cover of "Can't Get you Out of My Head" by Kylie Minogue. The occasional pop trash makes me all the happier, and this strange loungey/electro cover works fine for me.
And that's what I have to say about covers.