My wife does a pretty damn good cover of
"Psychic Hearts" by Thurston. Of course Cat Power did a completely different version as well.
My favorite Sonic Youth cover ever is William Hooker's version of "Becuz". He totally deconstructs it, and it's awesome.
Second favorite: Camper Van Beethoven's amazing country version of "I Love Her All of the Time". I first heard that unaware in a record store when it just came out and it freaked the shit out of me. EDIT: Damn, Chout scooped me on that one by seconds!
The best track from Confuse Yr. Idols is Steel Pole Bathtub's version of "I Dreamed I Dream"
I remember reading a review in Flipside ages ago about a dance band of some kind covering "She Is Not Alone", but I don't remember who it was.