I found this song the other day when I tried to google Bella's Lullaby (sorry about the Twilight reference). I hadn't seen the movie yet, but just finished the book, and was curious to see what the lullaby sounds like. Turns out this video isn't the actual lullaby, but there seem to be many many people who made videos on Youtube with Twilight clips accompanying the song. It's such a lovely tune, and I am actually glad it is not from the movie, so I can have it played in my wedding someday.
"River Flows In You" by Yiruma.