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 here, which is probably the single most moving ending to any 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 in one of the most heartwarming and breaking scenes in literature over 1000 players from the game put aside any conflicts and come to say goodbye to the Absolute Sword (or Zekken in Jap), 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. Excuse me I need a moment...
It's even more heart-rending in the anime. It's impossible not to tear up or cry as you see this one event. 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...Once again I need another moment. Need to get some tissues...
"Red-Nosed Reindeer", one of the sidestories. 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.... and learns 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.
Guess what story is the basis of Episode 3 of the anime? You will never think of the song mentioned in the title the same way again.
Specially heartbreaking the moment when Sachi actually 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. You can argue the story is rushed for trying to fit everything in one single episode, but that specific moment totally knocked it out of the park.
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.
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 BSOD 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 rather different reason.
Speaking of which, the ending for the GGO arc (Startear) seems quite beautiful... but then you read its lyrics, which 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.
The Alicization Arc, which has Eugeo dying, Cardinal dying, Charlotte dying, all within a few dozen pages from one another. Eugeo's death breaks Kirito, who blames himself.
And at the end of the volume Kirito's brain damage gets worse to the point where he's confined to a wheelchair and mute, even though he's still inside Underworld. The cover of the next volume portrays the sadness quite nicely.