Not forgetting that Thin Lizzy - Whiskey In The Jar is (technically) a cover of a folk song, and that is awesome.

Arctic Monkeys - Love Machine is a good cover
Flyleaf - Stay (Far Away, So Close), mainly cause I HATE U2
I much prefer Jimmy Eat World's cover of Firestarter by the Prodigy.
Word Up - KoRn is better than Cameos.
And finally, Triviums cover of Iron Maiden is pretty good, not better than the original though. Maybe on par? Just like Machine Heads cover of Hallowed Be Thy Name.