Jack Johnson - A Pirate Looks at 40 (Jimmy Buffett)
This actually hasn't been released on a studio album, but you can
download it free from Jack Johnson's website. (Yes, I know it was on The September Sessions soundtrack, but it's the same version that you can download, which was recorded from a KFOG concert back in 2001 or 2002).
Dave Matthews Band - Along the Watchtower (Bob Dylan)
The best version is from the Golden Gate Park concert on September 12, 2004, when Carlos Santana joins them on stage. I've been listening to Dave cover this for years trying to figure out what was missing, and it turns out it's Santana. (I have a torrent of this concert, if you're interested find me in the IRC channel or send me a private message).
Gipsy Kings: Hotel California (The Eagles)
Done with a flamenco/rumba twist. Sung mostly in spanish, with a little bit of english in the chorus. This is the song that plays in the background of
The Big Lebowski when Jesus rolls.
I have other favorites, but they've already been covered on this list.
Oh, the worst cover ever has to be the Madonna version of "American Pie." Blech.