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Tear Jerker: Fantasia
From the original, Ave Maria: There's just something about this mix of soothing and comforting animation and music immediately following the utter terror that was Night On Bald Mountain (not to mention the general intensity of the rest of the film) that it's almost impossible not to get a little choked up.
A bit of Fridge Brilliance, but Night on Bald Mountain/Ave Maria was based on dual concepts of the Judeo-Christian afterlife with the hell of Chernabog being contrasted with the heaven of Ave Maria. So the final scene of the cathedral leading out to the beautiful garden could be interpreted as someone's death and being welcomed to heaven.
While the music, animation and peaceful setting certainly do a lot to bring on the tears, the one moment that truly starts the waterworks is right when Julietta Novis comes in with her vocal solo. Her voice, combined with the rays of light that then open into the garden might just be one of the most simple yet profoundly beautiful moments ever committed to film or animation.
The death of the Adorkable Stegosaurus ("Evocation of the Ancestors").
The scene where the doomed dinosaurs are walking through barren wasteland under the endless burning hot sun in a futile search for water (to the tune of "Ritual Actions of the Ancestors").
Especially the T. rex. Just moments ago, the audience sees the world of the dinosaurs at its prime, during which all the herbivores flee in terror at the presence of the tyrant lizard king. Now, the T. rex is no longer a formidable creature and, in its futile search for water, now marches alongside the very creatures it used to perceive as prey... a sort of Enemy Mine, if you will. But for all that, their search is fruitless, and the mighty T. rex collapses from the heat and dehydration. The king is dead... the age of the dinosaurs is truly over.
Also, Firebird, somewhat, if you have a soft spot for nature.
The ending itself is so awe-inspiring it always brings this troper to tears, though that is as much Tears of Joy as this trope, when the sprite's sorrow and all the destruction turn into some of the most beautiful animation ever made which seems to palpably explode with celebration and wonder.
The baby whale who gets lost in the Pines Of Rome sequence
The Steadfast Tin Soldier's ordeal.
Most of the "story" pieces follow this structure: happy beginning, sad middle, happy end.
The "Firebird Suite" sequence in Fantasia 2000 - the Firebird's rampage is one of the most horrific scenes in Disney, and the ashen Sprite is a further blow...then the whole thing turns around as the forest is restored better than before (all accompanied by the glorious Stravinsky ballet music, natch).
The sprite restoring the beautiful tree that she had made after it was destroyed. And the soaring music through the whole end sequence.
Also from Fantasia 2000, the "Pomp and Circumstance" sequence about Donald Duck on Noah's Ark has a brief shot of a unicorn, dragon and gryphon pointing and laughing at all the other animals getting on the ark. The knowledge that those creatures were going to drown and never be seen again (shades of The Unicorn by Shel Silverstein) not only made me tear up, but deeply upset my then-six-year-old niece.
Both Donald and Daisy fail to witness each other get on the Ark before the flood sweeps away their home, so they believe their true love to be gone forever. Sure, they get back together in the end, but the idea of feeling so alone amidst a boat full of millions of couples is heartbreaking, and the parallels with An American Tail.
Another standout would be Donald trying to release the dove. The minute Donald turns his back the dove goes back to his mate, but Donald then grabs the dove and tosses him off the ark. The dove's mate then breaks down in tears, and you can tell from the look on Don's face that he immediately felt guilty about it.
The iceskating fantasy sequence in "Rhapsody in Blue".
Pretty much everyone in that segment is a woobie, but special mention goes to Duke, the construction worker who wistfully dreams of being a drummer; Rachel, the lonely little girl who wants to spend time with her parents; and poor Jobless Joe, broke, hungry, and desperate for work but unable to find any. Fortunately, things work out for all of them in the end.