I came to think about the art of making a great cover when i heard Carola on the TV. She made a song called Evighet (Eternity) for the Eurovision Song Contest 2006 and won in Sweden. Im not a fan of Carola, but the year after Tomas Andersson Wij performed a great cover of this song... and suddenly the song made sense! This is an example when the cover is so much better than the original. Watch them both below.
-- Which one is your favorite cover? --
Evighet - Tomas Andersson Wij 
Evighet - Carola