"Once Upon a December", a hauntingly beautiful song sung by Anya as she struggles to remember why the Romanov palace feels so distantly familiar to her. For bonus points, it uses the melody of the musicbox lullaby heard at the beginning of the film, making the song's subject matter even more powerful. That Truck Driver's Gear Change for the final verse is especially chilling. Even people who dislike the film for various reasons will admit that this song, and the sequence in which it is played, is one of the best elements of the film.
"Learn to Do It". The song is hilarious most of the time, but at one point, it freezes to show shock when 'Anastasia' gets something right that the other two haven't gone over: "I don't believe we told her that." Funny!
"At the Beginning", a wonderful and very memorable song that truly encapsulates what Anya and Dimitri find with each other once they get finally get together. Accompanied by shots of some of the best moments of the movie, and a lovely visual tapestry motif that reproduces Russian artistic design elements.
Prologue. Particularly the Ominous Russian Chanting and all the wonderful instrumental build-ups during the revolution, the struggle on the frozen Neva River, and the scene at the train station.