Lithium - the Polyphonic Spree (originally Nirvana). I think this one is just great, as the song is actually happy!
Or Placebo have done a whole albums of covers, which I think are rather good. I do like their covers of Running Up That Hill (Kate Bush), Bigmouth Strikes Again (The Smiths) and 20th Century Boy (T Rex).
Or, more obscure one's I like:
Paint it Black by Earth Crisis (originally Rolling Stones, also covered by many others)
Born in the USA - ballboy (Springsteen)
It Takes More - Mull Historical Society (Ms Dynamite)
I do agree that William Shatner's Common people is great, though I'm not convinced as to whether it's better than the original.