"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!
"Finale". Some of the most triumphant ending music ever heard, and accompanied by the wonderful visuals of Anya and Dimitri dancing on the boat, and finally, finally kissing.
"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.
"A Rumor in St. Petersburg" is insanely catchy and fun on the level of "Be Our Guest", and introduces Dimitri and Vlad amazingly.
"Land of Yesterday". Great, snarky comedy + wonderful performance.
"Stay, I Pray You". What they did with the tune of "In the Dark of the Night" - an incredibly emotional song reflecting on something that the movie didn't, their feelings on leaving their homeland behind forever. To make it even more emotional, Count Ipolitov - who leads the song - is double-cast with Anastasia's father. In addition, repurposing Rasputin's theme as antagonist into a song of farewell to the homeland (Russia) has the heartbreaking implication that the antagonist is now the homeland itself (the Soviet Union).