R.E.M.
I've heard them perform several cover songs, like "Don't Fear the Reaper", "Toys in the Attic", etc. plus several U2 songs, and they always sound great. They also did an excellent (and very funny) interpretation of "Tom's Diner" that I found back in the Napster days (since I absolutely don't download music now! Oh nooooo!
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Hmmm...seems to me that the musicians that do a good job with cover songs are the ones that are generally known for musical talent and insightful lyrics in their OWN music. Makes sense that the same talent (or lack thereof) would apply when they played other people's songs.