For me, playing a cover is about capturing a moment during a live performance, and giving everyone in the audience chicken skin when you break into that first riff.
That said, here's my two fav's:
Pearl Jam covering 'Keep on Rockin' in the Free World' (Neil Young) at the 93' MTV awards
&
Sublime doing the 'Guava Jelly/This Train Melody' (Bob Marley) from 98'