I love that Bing Crosby video. He just does not give a shit about the song he's singing.
Although it's probably because he's absolutely hammered and barely able to remember the words, let alone care about them.
I'd heard most of the others - the Andy Williams one isn't so terrible - but I didn't want to post too many examples, ruining the original forever.
Besides, have you heard Chris de Burgh cover Elvis Presley's In the Ghetto?http://www.youtube.com/v/LqMrveFhnZ0?