This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Legend of Galactic Heroes
It's practically IMPOSSIBLE not to cry in this series: its kill 'em all nature and extensive character development results in characters we have followed for hundreds of episodes, whom we have shared joys and sorrows with, to break our heart when they die.
The death of Kircheis. Even Oberstein failed to keep his cool when it happened (in part maybe because it was indirectly his fault).
The sad silence that falls following Yang getting news of Jessica Eduards death.
Reinhard fulfills his dream: his sister is saved, he now commands the Neue Reich, and manages to be a great leader. But the only two people he wanted to share it with are dead and not talking to him. And of course Reinhard not dying under equally thrilling circumstances, but instead a mere disease.
Even his beginnings weren't awesome. Born to poor nobles, he saw Annerose as a mother figure all because his mother got run over by a high noble and said high noble's family refused to apologize, making his father Sebastian resort to alcohol. Fortunately, he earned a friend in Kircheis, only for his life to get worse thanks to Kaiser Friedrich IV offering money to Sebastian so that he can claim Annerose, and claim Annerose he did. Yeesh, it sucks to be Reinhard.
Lt. Commander Jean Robert Lap clutching his fiances handkerchief as he lays dying an utterly avoidable death.
Schönkopf finally remembering the name of his daughter's mother as he dies looking down on his own carnage and the enemy soldiers cowering in front of him.
Yang doesn't die in a great battle, isn't outsmarted in tactics, or even killed by a named character. He bleeds to death. Worse, he does so all alone, and flagellating himself for all the people he's known who died in battle.
The reaction that everyone had at the news of Yang's death was heart breaking. Frederica's reaction was surprisingly calm at first, until she finally had an emotional breakdown.
Also, Frederica's comment on how she thought that instead of dying in such a horrible way, he deserves to pass away in peace after living a full life.
So does Reuenthal, out of his own free will. When he feels that the end is near he lays out a pair of drinks and waits for Mittermeier to arrive so they can share one last drink. Ironically Mittermeier, known for his fleet's incredible speed in combat, arrives too late. His reaction is heartbreaking.
In a powerful moment Reuenthal, calm and composed even as he's dying, finds himself moved to tears as he unexpectedly finds true happiness during his last hours of life.
Bergengrün used to be a jaded, disillusioned drunk before he was transferred under Kircheis' command. He develops immense respect for Kircheis, and pulls himself together in order to be able to serve him best. After Kircheis' death he ends up working under Reuenthal and serves him with deep respect and loyalty. When Reuenthal dies Bergengrün is so distraught over having lost not one but two brilliant and respectable commanding officers to political intrigue that he commits suicide, cursing the system and calling it rotten.
The scene between Mittermeier and Reinhard after Reuenthal's death, as Reinhard comes to the realization that from the people who faithfully supported him from the very beginning only Mittermeier is still alive.
Mecklinger delivering the sad news of Kempf's demise to his family. Especially so since we see the scene of Kempf bidding them goodbye as he heads to command Geiersburg.
Frederica Greenhill's reaction at discovering that her father was the leader of the military coup d'état on Heinessen was nothing less then complete disbelief and shock. Until the final resolution of the military coup, every time that she appears on screen afterwards has her staring blankly at the floor instead of being her usual self. Then, upon being told that her father committed suicide, she immediately stated visibly trembling and had to excuse herself from the bridge and suffered an emotional breakdown in her own private quarters, crying as she have flashback of happier times that she enjoyed together with her father.
Step One: Watch episodes 82 (In which Yang dies), and 83 (Which show how every Alliance character is emotionally broken from the lost of their beloved leader, but especially Frederica, who lost her husband after getting married for only a single year). Step Two: Re-watch episodes 51 (When Yang proposed marriage to Frederica), 55 (Yang's wedding), and 59 (Yang and Frederica simply enjoying their peaceful life as a happily married couple together). Step Three: Try not to cry. Step Four: Cry a lot.