Some more:

Hallelujah - Rufus Wainwright and Jeff Buckley, both better than the original IMO (Leonard Cohen)

Chris Cornell - Billie Jean (yes, Billie Jean. Originally by Michael Jackson)

Landslide - Smashing Pumpkins (Fleetwood Mac)

I Don't Wanna Grow Up - The Ramones (Tom Waits)

Helter Skelter - U2 (Beatles) - most will probably disagree, but I love U2's version.

Maggie's Farm - Rage Against the Machine (Dylan)

More to come...