The term "cover" does not apply to songs with no known author, IMO.

That said, there have been a number of excellent recordings made that celebrate the works of beloved songwriters, such as Love Gets Strange: The Songs of John Hiatt, several Richard Thompson tribute CDs, and Shawn Colvin's Cover Girl and Uncovered, which feature songs by Sting, Waits, Dylan and many more.

While the purist may feel that it's not possible for anyone's "cover" to surpass the original, I have heard many surprising and creative interpretations of well-known songs on those and other records. And however one may feel about Leonard Cohen's overused "Hallelujah", it would be hard to ignore the brilliance of Rufus Wainwright's version.