I like both versions but nominate:
You're not alone Mads Langer
(the original was by Olive)
I can also hear elements of Sia's Breathe me in it
talking of which The Wind and the Wave do a beautiful job of Chandelier
Also I adore the Lykke Li original but the cover was interesting
I follow rivers Triggerfinger
Cyndi did the brilliant Prince cover with When you were mine (her backing singer always reminds me of his version)
Frank Black's Down in the hole is totally different from the Stones
I also liked him and his wife's Cure covers contribution
Live lounge favourites:
Goldfrapp covering Not over yet
The Automatic covering Golddigger
Miley Cyrus covering Summertime sadness
Long before Live Lounge I enjoyed Dermot O'Leary's Re-covered on BBC choice. Radiohead fans will hate it but Liberty X's version of high and dry stuck with me
Doves also did a decent straight cover of the Smiths please please let me get what I want
Finally Seu Jorge's soundtrack to This Life Aquatic of Bowie covers should get a mention...whole album here