I don't know too much about various good covers, but I really enjoy the Wakey! Wakey! cover of Neutral Milk Hotel's "Two Headed Boy". And Jeff Buckley's "Hallelujah".
Jesse Lacey of Brand New also played a pretty good cover of 'Two Headed Boy'.
Mine would have to be:
Guided By Voices 'Gleemer' covered by Ben Gibbard.
Postal Service 'We Will Become Silhouettes' covered by The Shins
Don Henley 'Boys of Summer' covered by The Ataris
Currently playing: FFII (PSOne) & FFXIII (PS3) whilst his girlfriend fumbles through FFIV
'The man in black fled across the desert, and the gunslinger followed...'