To me, the best covers are when it's done completly differently, not just a band doing karioke. So:
Jimmy Eat World covering Firestarter by the Prodigy.
It takes about 2 minutes to realise that it's firestarter, it's so different.
A good one I heard was
by Oasis. Suposedly, Liam decided that was they way to sing wonderwall after he heard it.