Jeff Buckley's version of Hallelujah and Mama u've been on my mind. Original written by Leonard Cohen and Bob Dylan is up there in terms of cover versions, well in my opinion. Its just not a cover, he has rip round the basic structure of the song and makes the song sound completely different, im certain most of u will not recognise they r the same song even if u listen to it 1 after another.
I also find cover versions of Dylan songs always sounds better than when the great man sings it.
Surprise no 1mention the obvious 1, nothing compares to u, thats a cover version.
Also, its never been released but REM did a version of i will survive which is pretty good, i've got it on mp3, contact me if u r interested and Ryan Adams version of Wonderwall, which is a bit over rated but good none the less.