Hmm. Owen Pallett does a lot of good covers. My favourites being his cover of OMD's first four songs off of Dazzle Ships, and Jan of Arc's "The Hands". He also does an excellent version of "This Modern Love" by Bloc Party.

And then some more (original band/performer in brackets):
Les Mouches - "(They Long To Be) Close To You" (Carpenters)
Polmo Polpo - "Kiss Me Again And Again" (reinterpretation of an Arthur Russell song)
Animal Collective - "Polly" (Nirvana)
Feist - "See-Line Woman" (Nina Simone)
Stars - "Fairytale of New York" (The Pogues)

Uhmm, that's all I can think of.
EDIT: All of these are good. I can't think of some bad ones.