"Blood of Eden", especially the Carnivale fanvid, is cover of The Magnetic Fields "The Book of Love". The song earns extra points by being pretty darn hilarious as well.
One Word: "Biko".
The quiet, ending section of "Family Snapshot" (a song about Lee Harvey Oswald, or someone similar).
All turned quiet. I have been here before A lonely boy, hiding behind the front door Friends have all gone home...there's my toy gun on the floor Come back Mom and Dad You're growing apart, you know that I'm growing up sad I need some attention I shoot into the light
"Don't Give Up" is a prime example. Sounds like a cheesy title, but the lyrics, melody and Kate Bush doing supporting vocals all make it really work.
And then there's Shannon Noll and Natalie Bassingthwaighte's cover...