A couple of Kristofferson songs 'Me and Bobbie McGee' my current favorite is by the Grateful Dead and 'Sunday morning coming down' by Cash
Beyonce' does a fine job with several Etta James songs on the soundtrack of Cadillac Records.
I figure if the cover is so good, that a significant portion of the listening public doesn't know who the original artist that created the song is, then it's got to be in the "Best covers of all time" list.
So, "Bobby McGeee" and "Respect" would be my top two.