Covers that are better than the original

[savisn]

Better -

All Along the Watchtower
Landslide - Smashing Pumpkins (like it a bit better than the original Fleetwood version)
Mad World - Like Tears for Fears but not their version
Nirvana covers of the Vaselines
Jolene - White Stripes
Galaxy 500 - Don't let your youth go to waste (Jonathan Richman's version is good, G500 is amazing). Also Listen Outside the Leaves are Falling - better than Lennon/Ono version.
Superman - REM better than the Clique

On Par -

These are ones that are different enough to stand alone but I love both versions

Hurt - NIN = pain of drug addiction. Cash = pain of aging and losing his wife - both amazing
Nirvana covers of Meat Puppets and Bowie
Just Like Heaven - Dinosaur Jr. cover of a Cure classic is so different and great
Sweet Jane - Cowboy Junkies on par with VU

One that pisses me off most when others inevitably cite it - Hallelujah buy anyone other than Leonard Cohen. There are a million good covers but the original is perfect.