This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Blue Exorcist
Blue Exorcist starts out with the protagonist's adoptive father, Fujimoto Shiro, committing suicide to prevent Satan from taking him away. Later on, he and his brother find Fujimoto's familiar, a cait sith named Kuro, who has gone berserk upon hearing about his death. He refuses to accept it until the protagonist head butts him and offers friendship - just like Shiro had when they first met. Kuro breaks down into tears as he realizes his friend is truly dead.
Rin: It's okay. I bet you really loved my dad, didn't you? Thought so. And all this, it's just because you're sad, isn't it? Know what? I'm sad about it, too. (Offers his hand) So how 'bout we be friends?
Fujimoto's death got taken Up to Eleven in the anime adaptation. Up until that moment, Rin called him "Old Man", and before the possession, he told him to never act like he's his father again. While trying to drag him out of the Gate to Gehenna, he desperately screams "DAD!"
His death is made even worse due to what Yukio told Rin: Fujimoto was strong enough to fight off Satan's possession, but when he heard what Rin said, his defenses slipped. That means it was Rin's fault. Ouch.
Actually it's not Rin's fault - there is a few seconds in the anime and a panel in the manga where Shiro looks at the hand he slapped Rin with. And then he's being possessed. In other words, Shiro loves his sons enough that actually harming Rin for whatever reason is the worst thing he could do. But Rin doesn't know that and so ends up believing that it is all his fault. Not helped by the fact even Yukio places the blame of Shiro's death on him.
In the anime's special, Kuro leaves home in search of Shiro's grave, and imagines his spirit talking with him and consoling him. It's depressing, to say the least.
Usamaro the rabbit demon in The Movie. All he wanted was for everyone to be happy and forget their sad memories, and he ended up being sealed away for it.
And at the end, his Heroic Sacrifice and the fact that Rin is the only one who remembers him.
Rin: "Usamaro.... I'll never forget."
Uke and Mike being burned to death by Shima. Izumo always thought of them as brothers to her. Which in turn makes the way they quickly turned on her near the beginning of the series seem much more tragic.
After everything she endured, Izumo was given the chance to see her little sister, Tsukumo, again after 5 long years. Turns out she's now living under a new name, Takara Tsukiko, and is happily adopted. Relieved that she is okay, Izumo gains the courage to talk to her. But Tsukumo's response isn't exactly what she expected.
Tsukumo: " ...Who are you?"
Yukio's slow and gradual loathing at being powerless over the course of the series. He's becoming more and more desperate to attain power that he's resorting to throwing himself into situations that will very likely kill him in order to awaken it himself.
Lightning's interrogation of one priest to unravel the truth about Elixir results in the priest dying. That priest was one of the men who helped raise Rin and Yukio, to where they consider him a grandfather-figure. Bon knows the truth of it, but is forced to hide it and the guilt eats away at him while they've lost another person they consider family.