Concrete Blonde has done a bunch of great covers:
* "Ship Song" - Nick Cave (Heather Nova's version is also good, as is Cave's own of course)
* "Beware of Darkness" - George Harrison
* "Everybody Knows" - Leonard Cohen
* "End of the Line" - Roxy Music
* "Little Wing" - Hendrix
Bryan Ferry (/Roxy Music) has done some nice ones too, including a bunch of old jazz age standards
* "Jealous Guy" - Lennon
* "Sympathy for the Devil" - Stones (a not quite serious version)
* "These Foolish Things"
Jeff Buckley did such a good job on Leonard Cohen's "Hallelujah" many people don't know it's a cover
Same with Rod Stewart's "First Cut is the Deepest," which is actually a Cat Stevens song.