This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Wolf Children Ame and Yuki
The death of the unnamed wolfman. The reveal is difficult enough, but the way it's handled is excruciatingly brutal.
Spoilers ahead: Handled is a very good term, since he died in his full wolf form, the guys tasked with picking the body up simply throw it into a bag and toss it into a trash compactor. The fact that Hana has to watch all this and can't even properly bury him is heart crushing.
Then Hana's following dream where she sees her lover waving to her across a field, she waves back happy to see him again only for him to turn around and walk away despite her pleas, before he turns into a wolf and disappears, as if to signal his departure from her life forever.
When Ame almost drowned trying to catch a bird, very much in the same way his father died. The sight of Hana hugging him so closely and crying, as if he was going to vanish if she ever let him go, is heartrending.
Ame and Yuki arguing over their choices to live as either human or wolf, devolving into them fighting each other in their wolf forms. Seeing Yuki scratched up and holding herself as she cries in the bath is just... ugh.
Ame's departure at the end of the film starts this way, with Hana desperately begging her son to come back.
Hana: But I still haven't done a single thing for you...
When Hana wakes up in the parking lot, the first thing she sees is Ame walking away with his back turned to her before he turns into a wolf and leaves, paralleling the dream she had of the wolfman after his death.
What makes this even more heartbreaking is Ame's response to that line. By this point in the film, he's been established as maturing into being a fairly aloof and stoic character. His response to that line is one of being near to tears.
It seems he's become so lupine that he won't even speak. He just looks back at his mother regretfully, then runs away into the forest, presumably with no intention to ever return. Then he runs to the top of a mountain and just howls. Fortunately, there's a good chance he was simply showing Hana that she did plenty for him and the epilogue manga reveals he occasionally comes back to visit. Which is honestly pretty relieving.
"The magic words didn't work no matter how many times I tried." Yuki completely breaks down in tears in Hana's car after she had accidentally hurt Sohei. She can't hold back her sobbing AT ALL, and it cuts straight to the heart.
Masakatsu Takagi's "Okaasan no Uta" (Song of Mother). Dear lord.
I can do it for you. Is there already nothing left?
Someday, when you start your journey, I'll be sure to smile and see you off.
But I will be a bit lonely.
A Fridge Horror tear jerker. At the beginning of the day of the huge rainstorm, there's brief interaction between Yuki & Ame before Yuki goes to school. Ame asks Yuki to stay home that day and keep their mom company, Yuki declines, and then she leaves. This is obviously heart-wrenching, first of all, because Ame has probably decided by this point that he's gonna run away, and also because he knows it's going to storm badly. He doesn't want Hana to be alone and have to deal with all of that. This in itself is both a Tear Jerker and a Crowning Moment Of Heart Warming, but it gets even sadder with the Fridge Horror. That small, seemingly insignificant interaction between the two siblings is the last time they ever see each other. Yuki and Ame never got to say goodbye...
Seemingly. There's still a good chance they end up seeing each other again at some point. Especially with the epilogue manga revealing that Ame visits Hana occasionally. After all, Yuki is the narrator. She can't really tell a part of a story she knows nothing about. Still, it's sad this is the least interaction they have in a long time.
The fact that Yuki never does regain her old love of science and nature. She starts out as a wild, active little girl who loves collecting animal skeletons, little forest items, and playing with live snakes and frogs. When she starts attending school, however, she adopts a more modest persona out of a desperate desire to fit in — and even her adult self frets that she "didn't know how to be a little girl" back then. While Ame's love of nature at least takes root before he begins to be bullied at school, Yuki's life lacks for the kind of encouragement a girl like that needs, and as a consequence, her interests are quickly shamed out of her.
The English dub of this film was not only the last film to involve Jerry Russell as a voice actor, but it was one of his last films period. He died three weeks before the film premiered in the United States. His dedication during the English dub's ending credits invokes a major tearjerker for those who have grown up listening and watching his roles.