This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Sword Art Online
In Volume 7/Mothers Rosario arc, the name for the guild "Sleeping Knights" doesn't mean much at first. But then you realize that most of them have a terminal illness, and their name is Sleeping Knights. Needless to say, it's heartbreaking.
Volume 7. All of it, both good (Asuna's reconciliation with her mother, Kirito's Big Damn HeroesYou Shall Not Pass, every damn heartwarming moment between Asuna and Yuuki)and heartbreaking.
Special mention has to go out to the end of the novel. Yuuki is finally succumbing to her lifelong battle against AIDS, and Asuna convinces the Doctor to let Yuuki log into the Medicube one last time before the end. They meet at the same spot where the originally met, and Yuuki gives Asuna Mother's Rosario, her one of a kind 11 hit combo. Following this the Sleeping Knights guild show up and pay their last respects, and Kirito & Co. do the same. Finally, over a thousand players from the game put aside any conflicts and come to say goodbye to the Absolute Sword (or Zekken in Japanese), who fades away after thanking Asuna for all she did and saying "I tried my best to live... Here, I really lived...". And to top it all off at her Real Life funeral over 200 players arrive in the flesh, surprising everyone at the hospital who thought she had no friends.
It's even more heart-rending in the anime. The episode even drops the normal titles, just to make sure that the focus of the episode is this one event, the final minutes of the greatest fighter in the entire game.
"Red-Nosed Reindeer", one of the sidestories and episode three.
After Kirito joins the Black Cats of the Full Moon, they all get annihilated, including Sachi, a girl who reminds him of his sister, and someone he swore to protect. He goes through plenty of shit to find an ultra-rare item that's supposed to resurrect dead players, and eventually gets it with the help of Klein and Furinkazan, only to learn it only works for up to ten seconds after death, the amount of time it takes once their avatar shatters for the NerveGear to destroy their brain. By that point, Sachi has been dead for six months.
Sachi hums the song while Kirito utterly breaks into Manly Tears. Bonus points for the darkly sad and lonely atmosphere of that inn room during Christmas Eve. Sachi was his first love, especially in the web novels, regardless of what he says about that. Dude watched his first girlfriend die in front of him, just a few seconds before he reached her position. While they were not in a relationship, the word choices he used (in the original Japanese, at least) strongly implies he was in love with Sachi. But he recognized that emotionally above love, they were first and foremost Living Emotional Crutches for each other. Like two Broken Birds hanging onto each other for comfort. Which makes her death and his subsequent breakdown even more tragic.
Kirito does not expect to survive the quest for the ultra-rare item that will survive Sachi. He thinks he deserves to die in the attempt for such a failure. If Klein's offers of help sound like he's trying to talk someone out of jumping off a ledge, that's because he is.
Think about it: This dude, the token lech in the main cast, convinces his friend not to leap off the slippery slope of death-seeking. And this troper would be damned had he not succeed.
Pina's death is heartbreaking, especially to pet owners.
Episode 22 has Leafa guessing who Kirito really is. Leafa/Suguha was preparing to forget her love for Kazuto by trying to love Kirito. She entered a brief Heroic B.S.O.D. when she finds out Kirito=Kazuto.
Kirito's first attempt to charge the barrier over the World Tree is heartbreaking. Even as he bounces off of it, he just repeatedly throws himself at it, showing just how desperate he is to reach the woman he loves. Not to mention the sight of Yui pounding her hands on the barrier, frantically calling out for her mother.
Leafa: [struggling to stop him] Stop it Kirito, it's impossible! You can't get any higher from here-! Kirito: [cutting her off, nearly in tears] I have to!Damn it, I have to try! Yui: [desperate] Mama! I'm here, mama! [breaking into tears herself] Mama!!!
His initial solo fight against the Guardians is both this and awesome. He's pushing with everything he has, more aggression than he showed even in his fight against Heathcliff, as memories of Asuna flash through his mind. With every one he sees, the more aggressive he gets. He wants to see his wife terribly and it shows.
Speaking of the episode, Suguha only tells him to leave her alone in the Japanese dub. If you look at the English dub:
Episode 12. That is all. Yui's reveal and Disney Death. She comes back in ALO but still.
Also serves for plenty of in-universe example. Just when Kirito and Asuna were starting to feel like a real family. Asuna crying in sadness only amplifies this.
Episode 13: Just as Kirito tells Asuna to stay back at the guild headquarters, she refuses, telling him she'd kill herself if Kirito were to die. After he admits that he'd rather run away with her just so they'd continue to live with each other, she reminds him that their real bodies don't have much time left. She then begins to cry in his arms, saying that she wants to live together with him in the real world.
The second half of Episode 15. Kirito learns that Sugou is planning to make Asuna his and tells the boy never to see her again. He is completely in tears in the subsequent scene, crying against Suguha's shoulders. Later we see Suguha lie beside him as he sleeps, shedding tears as well, but for a ratherdifferent reason.
The whole situation of Sugou/Oberon sexually assaulting Asuna in front of Kirito in Episode 24 is Nightmare Fuel, but it's also pretty grim on another level. Kirito is so close to saving Asuna, when suddenly, Oberon cuts the reunion short and spams his Game Master status, pinning Kirito on the ground with gravity-based magic, chaining Asuna, and then as Kirito tries to get up, Oberon impales Kirito with his own sword and then procedes to tear parts of Asuna's garments off, and then states that once he assaults her in in the virtual world, he'll do the same thing to Asuna in the real world, while she is in a coma, in her hospital bed, and Kirito would be unable to prevent it. After saying this he proceeds to lick her and do all sorts of nasty things to her, while Asuna starts crying in despair. Heck, Kirito, in his Near-Death Experience basically sheds a tear and completely gives up (in his words "facing reality"). If it hadn't been for Kayaba's spirit showing up and lending Kirito his system administrator status and giving him a Heroic Second Wind, Sugou would've gotten away with everything! And this would've resulted in a Downer Ending.
Speaking of which, the ending for the GGO arc (Startear) seems quite beautiful, but the lyrics fit Shino's state of mind during this arc so well that it's quite heartbreaking.
When Kirito runs into Death Gun and learns that he is from Laughing Coffin from SAO, he's so shaken, that when Sinon comes to check on him, he grabs her hand as she's about to leave, as if pleading her not to leave him. This continues on until his match with her where he's lost the will to fight and nearly throws the match.
The ending for the Mother's Rosario arc in the anime. The song is beautiful yet sad and the scenes it play through feature Asuna and Yuuki hanging out together. It's implied that Asuna is reminiscing about Yuuki after her death.You don't even find out whetherany of Merida's guildmates survived SAO.
The side story, Sister's Prayer, essentially a prequel to Mother's Rosario. Not only does it drive home how hard life can be for Yuuki, Ran and their new friend Merida, but there's also the Foregone Conclusion about how all three girls succumb to their illnesses in a year or two, and Ran died sooner because she insisted that Yuuki test the Medicuboid, which allowed her to get a clean room.