Here are four songs I recently downloaded. Don't care about the videos, the music makes up for anything lacking there.
Paul Potts: Nessun Dorma
http://www.youtube.com/watch?v=GOKsoORWZisI never gave a rat's ass about opera, couldn't stand it actually, until I heard him sing this.
He seems like the most lovable person. His shyness and unassuming nature makes his story all the more heartwarming. You can't help but cheer for this guy to achieve everything he wants. I just want to walk up to him and pinch his little cheeks

Andrea Bocelli: Because We Believe
http://www.youtube.com/watch?v=alRXR0ogz3sI didn't know until very recently that he was blind. He makes me want to learn Italian

Celine Dion: Taking Chances (a good old ballsy song

I didn't know it was a remake though)
http://www.youtube.com/watch?v=RhtdXu1rc_0It ends on an odd note though :-\
Hardly of the same calibre, but I love this song too. Daniel Powter: Bad Day
http://www.youtube.com/watch?v=oIcFgl6zf3A