Excellent thread Amanda. I could very easily post in here all day long, but I will limit myself for now to a few examples of good and bad.

Good:

Time Is Tight - The Clash (original by Booker T. & The MG's)

The Clash do a fine rendition of it, particularly in Mick Jones' formation of chords to make up for the obvious lack of Booker T.'s organ.

Paranoid Android - Brad Mehldau (originally by Radiohead)

For those of you unfamiliar with Brad, he is a jazz pianist, and one of a caliber I can only compare to players like Thelonious Monk and Keith Jarrett. He has covered several Radiohead songs over the course of his career and does a fine job on most of them, but this one in particular is very impressive. It is a difficult song to appropriate in a solo piano version, but he does a remarkable job. Perhaps the only cover that he has done which has impressed me more is his absolutely stunning version of The Beatles' "Dear Prudence."

Sittin' In Limbo - Jerry Garcia & David Grisman (originally by Jimmy Cliff)

While I still prefer the original (Jimmy's voice is so powerful to me), Jerry & Grisman's version is fantastic. Their playing is spectacular and Jerry's voice is very well suited for this song.

Bad:

Knockin' on Heaven's Door - Eric Clapton (originally by Bob Dylan)

I know a lot of people like EC's version, but for me the original is the ONLY version of this song. Short story, I was once on a date when Bob Dylan's version came on the radio in the car. The girl I was with commented that "it's ok, but it's not as good as Clapton's original version." I was quite tempted to pull the car over right then and there and declare the date over.

Dear Prudence - Jerry Garcia Band

I love Jerry, but this one just never worked for me. For starters, I've never heard a single version where he gets the words correct. Secondly, it just doesn't go anywhere musically. I am not one of those who gets on Jerry's case for "noodling" on the guitar because many many of his solos have structure and cohesiveness. Unfortunately, on most versions of Dear Prudence, this is not the case.