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Tear Jerker: Pokémon: Lucario and the Mystery of Mew
Aaron's final monologue, which ends with Lucario breaking down in tears at the fact that Aaron thought of him as a friend and everything he thought about him was wrong.
James' first instinct when being devoured by the Tree's defenses is to release his Pokémon so they don't suffer his fate. The heroes follow his selfless example when they get eaten, as well.
The circumstances of their getting eaten are pretty tragic too. First you have Jessie getting eaten right in front of James, who is unable to save her and even gets a Big "NO!" in as she "dies" before he is eaten as well. Then May gets to see her little brother and Brock get eaten right in front of her, and - again - she gets a brief moment of despair before being taken as well. And finally there's Ash, and Pikachu's absolutely frantic attempts to pull him out before he disappears completely before breaking down in tears.
The Pokémon's anguish when they thought they lost their trainers from the Tree Of Beginning's "white blood cells".