This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Rave Master
King's backstory, all he wanted was to make the world a better place, even with some dirty means leading to Gale associating with the wrong people in the Empire to take him in, resulting in the deaths of his wife as well as his son, though the latter actually survived to be imprisoned for ten years; even though killing Gale's wife and Haru's mother was bad It's very tragic to what happened to him.
Sieg Hart tortures Elie with lightning and tries to pull an Hannibal Lecture on her, telling her repeatedly that she's just Experiment 3173 and that she should just let him kill her. Elie is about to accept this as true... until the flashbacks to her childhood and her connection to Resha Valentine kick in. But she's already so weakened and injured that she simply can't fight back.. And then, Haru comes to rescue her, but can't do anything but hold the almost fatally injured Elie in her arms as she falls into a coma and he thinks she's dead. Cue to him screaming Elie's name. SOOOOOOB.
While trapped in a Stable Time Loop in the past, Sieg Hart sent Haru and Elie who we now know is Resha Valentine back into the present, at the cost of him remaining in the past for good. Before he sent them, he wished Elie that he wished her a happy life. And knowing what he had did to Elie before (just see the above), it is both a Crowning Moment of Heartwarming and a Tear Jerker.
But the real Tear Jerker comes as Sieg waited alone by Resha's grave, knowing he can't meet with anyone in case he altered the present, he incidentally met up with Resha. She was holding a necklace that had belonged to Elie. He asked her for it, because he knew he would never see Elie again. Resha handed him the necklace and before she left, she told him that whoever the necklace belonged to, they must be really happy to have such a good man cherish their friendship. Then, he put on the necklace and sat down in front of Resha's grave to do the last thing he could for Resha/Elie. Remember the skeleton that the gang found way, way back sitting on the rock as if protecting Resha's grave? That was Sieg Hart. For fifty years, he watched over Resha/Elie's grave, long even after his death. Haru and Elie's expressions as they realized who the skeleton is was utterly heartwrenching and painful to see.
Also when Lucia has a flashback of being found immediately after his mother was murdered in cold blood. You can hate him all you want, but if you didn't cry when you saw the misfortune he experienced as a child, you have no heart.
The tenth form of Decalogue - Dark Emilia.
Really just the whole general revelation that he's not half as unfazed by the crap he's been through as he pretends. His real goal is even to be able to live a normal life, unaffected by the curse in the current world that drives him to be alone.
The death of Gale Glory. Guy just reunited with his son and they talked before about how they would both go back to Garage Island once King was defeated because Gale needed to keep his promise with Cattleya. Later, the tower is collapsing on them and after telling Haru about Star Memory Gale goes right over him, stating that saving Haru is more important than keeping his promise. Dammit, Mashima! You bastard!
An earlier example of this was Gale letting an exhausted King, who had lost his mind as a side-effect the dark bring Monster Prison, futilely hit him because it made King feel better. After all King has done Gale still cares for his best friend enough to shoulder all his hatred but you can tell it is breaking his heart.
The flashback episode "Origins: Shiba", where Shiba tells the story of how he became the first Rave Master was very sad at the end. Shiba's anguish at the idea of Resha being dead and gone can really bring on the waterworks. Of course she wasn't dead after all but, somehow that kinda makes it worse!
Especially because while in the past, Elie after remembering she is Resha, finds him crying over her "death" and starts going over to him but is stopped.
Anything that involves a character's past, really —- save for Griff, of course.
Doryu's past is extremely heartbreaking; he just wanted to build peace between his people and humans, only to have his work spit on by racist bastards, the village he made taken over by human supremacists, and the same boy who enthusiastically greeted him call his dreams disgusting and unnatural, before being locked up in prison for no real crime. Needless to say it's impossible not to understand his hatred of humanity and his contempt for the light worshipers as a result of this.
Jegan's Heel–Face Door-Slam. After Let defeats him and saves Julia, he washes up on a beach and is nursed back to health by a cute villager named Jana. Jegan is in despair over losing to Let and over losing Julia and attempts suicide, but his estranged brother and Jana manage to talk him down. Just as it looks like Jegan will move on from Julia and get together with Jana (he even offers to show her a real dragon), the village gets nuked by Shakuma. Jegan's brother finds Jegan's dead body covering Jana's in a futile attempt to protect her.
Branch's Heel–Face Door-Slam isn't much better. Yeah, the guy was a slimy little prick, but all of his problems stemmed from the fact that he was a coward. By the time Koala transforms him into a machine, he's just a pathetic wreck of a man begging for help and asking to be killed because he can't control his new body. He knows he hurt a lot of people as a man and doesn't want to be forced into hurting even more as a cyborg. While he still tries to excuse his behavior, Haru is able to give him the courage to fight his body's overriding commands, Haru, in a rage, chases down Koala and orders him to fix Branch which is all but impossible. Branch then seeks out Haru and informs him that the Blue Guardians plan to blow up La Résistance with a hidden bomb and that he should leave. Upon escaping, Haru realizes that Branch IS the bomb and that he stayed behind to save them. With Haru screaming his name, Branch dies wishing that he had been Haru's friend for all those years all while crying. Jeez man.