On the topic of good covers:

John Mayer covered "Kid A" very well. I would say it's very, very close to the goodness of the original, which elevates John Mayer in my view.

Ahmet and Dweezil Zappa covered "Baby One More Time" by Britney Spears. Needless to say, the Zappa's version is cooler (now if they could have worked in Moon Unit in there, that would be a hat trick)

I like Alien Ant Farm's cover of "Smooth Criminal" better than Jacko's.

Every song that Nirvana covered in their Unplugged set, especially the Meat Puppet's stuff.

I can't decide of Johnny Cash's cover of Hurt is better than Trent's. Very, very heart-wrenching, that one. Why is it that he can sing about things he's never experianced and make it sound so beliveable?

Other covers that are better than the original:
Joey Ramone's - "What a Wonderful World".
Mike Ness - "I Fought The Law"
Fiona Apple - "Across the Universe"
Dixie Chicks - "Home"
Matthew Sweet - Scooby Doo Theme
Rage Against The Machine - "How I Could Just Kill A Man"
Violent Femmes - "Do You Really Want To Hurt Me"
Presidents of the United States Of America - "Kick Out The Jams"

Well, that should do it for now.