"Dancing with Myself", Nouvelle Vague
"Beauty & Madness", MYMP
"Rebel Rebel", Seu Jorge
"How Can You Mend a Broken Heart", Al Green
Those are the first that come to mind.
Oh, and Phoenix's covers of their own "Lisztomania", "1901", "One Time Too Many and "Long Distance Call". I don't know if that counts, but in my book it does. Same thing goes with Bloc Party's acoustic cover of their song "This Modern Love".
"Oh Well" by Joe Jackson.
(Actually, I'm not sure if it's a favorite; but it'll do for now.)
"The Man Who Sold the World" by Nirvana was all I could come up with.
The Flakes Coverin "Open Up your Door" by Richard and the young lions