All Dogs Go to Heaven: The very end after Charlie has died for the second time and is allowed a chance to say good-bye to Anne-Marie. The whole good-bye is sad enough but the "I love you, too" is just...
The ending scene hurts especially when Charlie tells Anne-Marie he's going on a trip and she asks if she'll ever see him again. It's like a parent trying to explain to their child that they're going to die soon.
Anne-Marie: Charlie, will I ever see you again?
Charlie: Sure. Sure you will, kid. You know, good-byes aren't forever.
Anne-Marie: Then good-bye, Charlie. I love you.
Charlie: Yeah. I love you too.
In Anastasia, after Anya and her grandmother are reunited, the camera cuts to Dimitri blowing a kiss through the window and walking off.
Also, when Anya finds out about the con, Dimitri's face is a combination of desperation, regret, and wanting her to see that it's not like that now.
"Once Upon a December." The poor princess didn't get to have her palace and her dresses and her life...
And once Anya and Dimitri sort their differences and stay together in the end, these tears of sadness become tears of joy. The story might screw up history bad, but still... It is all part of the whole tragedy of it all. You can debate till the cows come home whether Nicolas was a bad ruler, whether monarchy is overrated and needs to be done away with, and exactly who it was who screwed up Russia's future, but the simple fact is, Anastasia did nothing wrong. Rather like Marie Antoinette, her only crime was being born in the wrong family, at the wrong time in history, and being blamed by the (rightfully) angry common citizens for all their troubles. The "Once Upon a December" sequence highlights the fact Anastasia was not just a princess, but a person who lost her whole family through no fault of her own, and only wanted to have it back. Granted, there's a bit of the wish fulfillment for a 'golden age' and 'lost grandeur' in there too, but even so... The deeply tragic Real Life subtext makes the whole movie a bit of a I Wish It Were Real moment. All politics aside, the Romanov's didn't deserve what happened to them.
A related moment to nominate: after Anya and her grandmother are reunited and reminiscing about their family, looking at a picture of them. The dowager empress's words about their lost loved ones not wanting them to grieve were especially poignant.
And also, the fact that Anya's drawing was drawn by the real Anastasia is both touching and sad, especially knowing that she wasn't as lucky as her animated counterpart.
In Titan A.E., when you think Goon died saving Stith from the bomb Preed planted in her wrist communicator.
Finding out for sure that Cale's father was dead was even worse.