I think "All Along the Watchtower" is widely considered to be the best cover song of all time.

I've always had a soft spot for John Denver's cover of Ian & Sylvia's "Darcy Farrow," myself. Also his cover of Eric Andersen's "Thirsty Boots," which I think is better than Judy Collins's try at it, even though hers was a hit in the UK and his was never really popular with the general public.

EDIT: "Listen to Grace's rendition of Sting's "Demolition Man" and tell me that Sting's version is better?! I thought so.

Demolition Man
Sting cover."

That was utterly, utterly terrible.