if you're into Folds's "Bitches Aint Shit", i'd also highly reccommend his cover's of "Get Your Hands Off Of My Woman," and "In Between Days."
i can also suggest...
"We Will Become Sillhouettes" - The Shins (...surprisingly, NOT on the garden state st!)
"BK Baby" - Ben Kweller (his version of Ice Ice Baby...)
"Here Today, Gone Tomorrow" - Rooney (...this is one of my favorite covers ever.)
"I Found A Reason" - Cat Power
"Road Runner" - Joan Jett and the Blackhearts
"Where Is My Mind?" and "If You Leave" - Nada Surf
"Helter Skelter" - Oasis (there are actually about nine different versions of Helter Skelter on my iTunes. i also really dig Siouxsie's cover...)
"Spit On A Stranger" - Nickel Creek
"Wave Of Mutilation" - Rhett Miller + Ben Kweller (that one's live...)
"Accross The Universe" - Rufus Wainwright
"I Just Don't Know What To Do With Myself" - The White Stripes
everything else has been mentioned already pretty much...