Human beings are emotional creatures; it's the nature of human existence. It's not a shameful thing, just a truth of life. Successful entertainment medias capitalize on that. Strong narratives build emotional connections between the audience and the source material.
This can be espeically hard in an animated medium, as it can be harder to draw parallels between ourselves and characters that aren't strictly 'real'. It makes it that much more powerful, though, when they succeed. Here's a few times they did.
The Nina Chimera - Full Metal Alchemist
Let's just rip this band-aid right the hell off. This scene was so monumentally soul-crushing that you just had to take a step bnack from the viewing to recollect yourself. Over the course of but a SINGLE EPISODE you built an emotional connection to Nina and her father's plight, his failures in his research. You saw their struggle as a broken family, but you knew, somehow, things would turn out okay.
WELL THEY REALLY GODDAMN DIDN'T, DID THEY? THINGS GOT A WHOLE LOT FUCKIN' WORSE FOR NINA. SHOU TUCKER YOU GIANT PIECE OF HUMAN GARBAGE HOW COULD YOU DO THA-
Pikachu Shaking Ash - Pokemon: the Movie
The first Pokemon movie, (you know, the one with Mew and Mewtwo duking it out in super-powered style) was a masterful work of animated fiction, especially for the long-ago days of 1998. It tackled some pretty heavy issues, like identity, quasi-race issues, and the importance of love and trust. It was the best.
Then, with the ending of the film, it dropped what is, for so many, the most emotional scene of your childhood. Running into a calamitous fight between original and cloned Pokemon, Ash winds up caught in the middle of two powerful energy blasts between Mew and Mewtwo, turning him immediately to stone.
In the most tear-jerking scene in all of Pokemon history, Pikachu runs over to his fallen friend, abandoning his own fight. Unable to accept Ash's condition, he begins shaking him back and forth, then shocking him, trying desperately to save his friend.
You cried in the movie theatre.
Mikasa's Backstory - Attack on Titan
As we know Mikasa for the first few episodes of Attack on Titan, she is a calm, collected individual, if a little distant. She's the level headed one of the the two siblings. She keeps Eren's emotions in check. She als ohelps look out for Armin.
The anime progresses a few episodes before we actually get her backstory, and at that point, we just want to reach out and bring Mikasa into our arms, hug her. We find out that her parents were brutally murdered by human traffickers attempting to kidnap her, as she and her mother were two of the last members of their race.
To think about what would have happened if they succeeded is too dark. Still, though, what happened was almost as dark. Eren kills two of the would-be kidnappers, and as the third overpowers him, Mikasa is paralyzed with fear. Coming the realization that the world is a cold, merciless place with no good in it, she murders the shit out of the last kidnapper, and is left forever emotionally scarred from the experience.
L's Death - Death Note
One of the most recognizable characters of all of manga and anime, L is the rude, eccentric detective in charge of determining who the killer, Kira, truly is. Throughout the anime, you see L get progressively closer and closer to the unmasking of Light as Kira, even as obstacles pile up in front of him.
For his eccentricities and his quirks, L takes a special place in the heart of all viewers. A direct contrast to Light, he is the beacon of intelligence, logic, and reason in the anime. He is entirely committed to the investigation, and believes from an early point that Light is the true identity of Kira.
He gets almsot to the point of unveiling Light, when Light pits the shigami Rem after him. In a high energy-high noise sequence, we are made to believe there is a chance of defense, until L dies, mid-sentence.
Everyhting goes quiet, Light catche's L's falling body. the last sight that L sees is Light's twisted smile, his rival having defeated him. As church bells toll and images of L's past flash through his mind, we finally see him closing his eyes - asleep at last.
Naruto Meeting Kushina - Naruto
A major part of Naruto's identity is the fact that he is an orphan. He lost both of his parents as he came into the world, and so grew up without parental guidance or the love of family. He was ostracized from his society, made into an outcast. He define himself in oppostion to all that, and managed to succeed as a shinobi in his own right.
He accomplished so much on his own, without having someone to clap him on the back in pride. he had mentors, yes, but none of that necessary parental love. Until he got to meet his mother.
Having put a portion of her own chakra into the seal that held the Nine-Tailed Fox at bay, Naruto's release of the seal prompts the spirit of Kushina to appear before him, in the meditative state he's in. So technically is was a vision of her, but she had full agency of herself. This moment was the most heart-wrenching of all the series, because there really is nothing like the love of mother and son, or specifically son for mother. And for him to finally, finally have the opportunity to just hug her and talk to her...
It made you heart swell to bursting size.