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Tear Jerker: Anastasia
Anastasia's dance with the Czar, her father, during her Disney Acid Sequence dance. No matter what opinion you have about Czar Nicholas II, the flashbacks and visions involving the family, Alexandra (the mother), the older sisters (Tatiana, Olga, and Maria), and the little brother (Alexei), strikes as heartwrenching considering what happened to the family in reality.
The reunion between Anastasia and her grandmother Marie.
This troper doesn't think that's a tearjerker (at least not in a sad way). I thought it was very touching when Anastasia and her grandmother were finally reunited.
Dimitri's reaction when he realizes Anya's true identity. The girl he's fallen in love with and thought was his equal is the real Grand Duchess. And they can't be together because he's a former servant and is now unworthy of her.
Perfectly shown in his defeated conversation with Vlad.
Vlad: That means Anya has found her family! And you—
Dimitri: Will walk out of her life forever.
Dimitri: Princesses don't marry kitchen boys.
Later scenes add to this: Him being forced to bow to her, refusing the money, and his expression when he sees Pooka holding her crown. No one's telling Dimitri he's not good enough for Anya - he just knows he is. The instinctive values here can't be emphasized enough. He was a servant at the beginning who admired the Princess but was never noticed. He obviously spent years trying to move past that, and now, because of a difference in title, Anya is unreachable again. They're still the same people, she's still the same girl he's insulted and saved and comforted, but suddenly that's it, he's just as inferior to her as when they were children. And he can't do anything about it.
As a troper who as a child had just assumed that Anastasia was a 100% made up princess, after I later discovered that this movie was based on a real person (and the true life and death story behind said person), despite this being a wonderfully made movie, it also seems like a cruel parody. Animated film-version Anastasia lived happily ever after with Dimitri. The real life Grand Duchess Anastasia was brutally shot and stabbed to death at the tender age of 17.
Any scene with the Dowager Empress Marie. Take out the whole revolution and royalty thing and all you have is an old woman who watched her son and grandchildren die.
The scene where they're trying to get on the train at the beginning. You can see there are tears in Anastasia's eyes during the part where she tries to catch up with the train and Marie grabs onto her granddaughter's hand, saying, "Take my hand! Hold onto my hand!" and Anastasia cries, "Don't let go!" However, they both lose their grip on each other's hand and Anastasia falls to the platform, hitting her head and getting knocked out cold, all while Marie desperately shouts her granddaughter's name and all the passengers are holding her back from jumping off the train to get to her.