This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Space Battleship Yamato
An early episode has the crew lined up to take their turns using the video phone to talk to their families left behind on Earth. It's limited so each crew member gets something like 1 hour every week. Derek Wildstar/Susumu Koudai (The Hero) isn't there for his turn when his name is called, so Venture/Daisuke Shima) (The Lancer) and Derek's only friend decides to go find him. He and Nova/Yuki Mouri (Derek's Love Interest) find Derek, and he tries to brush it off saying it's not important. They insist he talk to his family (after all, Earth is dying, and who knows how much longer they'll be able to stay in contact) and they physically drag Derek to the communication room. Venture is waiting for his turn outside with several other crew members when they decide it's rather quiet. They peak into the room, and see Derek staring at the blank screen. There's just this look on Derek's face, though Venture doesn't notice it as he begins scolding Derek for not caring about his family, and why doesn't he just talk to them... Derek's stoic face finally breaks and he yells back "Because there's nobody left for me to talk to!" His family and friends are all dead. Most of them died when Earth got Nuked, and his only surviving family member, his older brother Mamoru/Alex, had died in the first episode. It was just, wham. It's been 20 years since I saw it, at the age of 8, but I have never forgotten it.
When Derek was staring at the blank screen, it's Nova who's peeking in and wondering why he's just sitting there. She then asks him if there's a problem, and gets shocked when he replies: "There's no one for me to talk to on Earth!", and subsequently runs off apologetically. And earlier in the episode, it's revealed that only Captain Avatar was aware of this, thinking it to himself when he saw Derek running off somewhere. It got really heartwrenching near the end of the episode after Derek walks out into the bridge, and everyone looks at him with expressions of shock and pity while he just stares back at them with the same expression he's had most of the episode, before heading toward's Captain Avatar's quarters.
A later episode has a scene that ties in to the issue. The Starforce engage a squadron of Gamilon fighters and destroy all but one of them (which is left damaged and drifting), which they capture in order to interrogate the pilot. And when Derek sees the pilot, he goes into a rage over the deaths of his family and friends (shown in a subsequent flashback), and promptly starts beating up the prisoner. The latter's response? He tears up, with a look on his face that screams "Why are you hurting me?", which is enough to put Derek back to his senses. It's revealed that Gamilon pilots have their memories erased and stored till their return so that they reveal nothing to an enemy if captured. So in a sense, Derek ended up pummeling an innocent child.
How can you all forget the death of Captain Avatar? He goes through hell and high water to save Earth, and then dies just before seeing it again! And the only mourner he had was that goofy doctor!... Really, for a kid raised on mostly American animation in the late 70's-early 80's the death of a MAJOR SERIES CHARACTER was so shocking as to be earthshaking.
Venture had his own Tearjerker, as he was at the video phone talking to his family as they moved out of communication range. His family was trying to put a good face on whatever was happening back on Earth cause they didn't want to worry him, while Venture was doign the same thing for his own problems. The picture started to cut in and out and you could just tell, they were looking at each other, and suddenly there were all these things that they had put off saying to each other because it just wasn't the right time, and now suddenly, there was no more time, and they couldn't say it to each other anymore.
In the 2010 film adaptation, we see several of the crewmembers talking with their family at home. One crewmember's son is evidently mute and has to type to talk, the Space Marine has a mother who worries that he will catch cold, and so on. In every example we see though, as their allotted time runs out (limited so everyone has a chance to talk), the call is automatically disconnected before they can finish. None of the crewmembers shown talking to their families live to finish the conversations.
In the original Japanese, the speech Wildstar/Kodai gives about how sorry he is for utterly destroying Gamilon. Desslok gets one at the end of the second season when he gives a speech about how he had never loved and all he had wanted was to inflict pain. In The New Journey, the ravaged Gamilon explodes, and then Desslok's ex-girlfriend kills herself to stop him from killing himself and he completely loses it and starts screaming and pulling his hair and gnashing his teeth in an epic tear-jerking Freak Out.
Not to mention all of Farewell Space Battleship Yamato: Soldiers of Love. At least from Talan's death on.
The last 45 minutes are BRUTAL. But the last scene, with Kodai half between life and death, surrounded by Yuki and spirits of Yamato's crew as it rams Zwordar's ship are poetic and tearjerking.
The ending of the Live-Action Adaptation is one huge tearjerker. After losing most of the crew in the battle at Iscandar and obtaining the anti-radioactivity device, now imbued inside Yuki, the Yamato returns to Earth... and with them comes a giant space weapon created by the Gamilas, sent by Dessler to destroy the Earth. With the Yamato badly damaged, most of the crew dead, the Wave Motion Gun blocked by a Gamilas fighter jammed into the muzzle and only enough power left in the Wave Motion Engine to fire off one more shot, Kodai, as captain, orders all surviving personnel to immediately evacuate the ship. After knocking Yuki unconscious so she doesn't waste precious time, the remaining crew members evacuate in a space pod, leaving Kodai on the bridge of the Yamato to fire the Wave Motion Gun in a kamikaze divebomb run on the Gamilas weapon. Kodai accelerates the Yamato towards the weapon, and back on the space pod, Yuki gains consciousness to see the Yamato, sparking and burning, heading towards the weapon with Kodai onboard. Yuki, distraught, yells Kodai's name furiously, begging him not to die and to return to her. On the Yamato, Kodai locks onto the weapon and, in his final moments, the departed souls of the deceased crew appear before him, and salute him, seeing him off and letting him know that, yes, the Earth will finally be saved. As the Yamato plows bow-first into the weapon, Kodai pulls the trigger on the Wave Motion Gun, whispers "Yuki"... and a brilliant light fills the sky as the film fades to black. As the credits roll and Steven Tyler's Love Lives plays to a montage of the Yamato crew's many hardships, we fade to a gorgeous countryside, grass billowing in the wind. Yuki stands, looking outward to the restored Earth... and her and Kodai's son, who was conceived during an off-screen night of passion earlier on in the film, calls out for her, shouting "Mama!! Mama!!" Yuki goes to her son, and the screen fades to black once more.
Not to mention the opening battle in 2199 where the Earth fleet gets completely curbstomped by the Gamilas. When the remnants of the fleet are forced to withdraw, Kodai's brother decides to stay behind to cover Okita's retreat. While that act in itself is sad enough, as Kodai's brother and his crew sail on to their imminent deaths, they start singing an upbeat song about sailing into the stars.
Echoing the scene, Gamilas reserve forces made up by veterans and untrained conscripts plus a few commandos from a second class race are preparing for a describe battle against Yamato. The atmosphere is gloomy, then one of the commandos started to sing the Gamilas anthem, followed by everyone else.
Episode 8 of 2199: Commander Shultz's final moments before his ship is destroyed while pursuing the Yamato and getting too close to a star - he recalls his wife and daughter whom he will eventually leave behind upon his death, considering earler, and in a previous episode, he was watching a hologram message from his daughter greeting him and telling him to come home after his tour of duty is done.