This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Hunter × Hunter
I never knew being weak could be so painful...
When we're first introduced to Leorio, the audience was made to believe that he was just some greedy punk because his motivation to being a hunter was Money, Dear Boy. However, at the beginning of the Hunter's Exam, Kurapika learns that he wants the money to be a doctor and run a free clinic after a close friend of his died at a young age. It makes his Funny Moments where he rants about wanting money Harsher in Hindsight.
During the arc where Gon goes to the Zoldyk household, the Battle Butler Canary stops them from progressing any further. Gon attempts to get over the line she sets, but she effortlessly knocks him away with her cane. He keeps getting knocked back over and over and over again, just to make it through, and she's having none of it. By the time sunset hits, she actually worries about his health and questions why he'd be stupid enough to keep crawling to the gates when he just won't pass, and all Gon answers with is the fact that Killua is his friend. Just when we think that she's going to have a change of heart and let him pass... Luckily, she survived the whole thing.
1999 anime. After Kurapika kills Uvogin, he falls to his knees and holds his head in horror. The next time we see him, he goes to his hotel room, and starts to chant the Kurata prayer slowly, traumatized. Poor guy.
Squala's death at the hands of the spiders. Considering the implications of Pakunoda's power, his girlfriend was the last thing he thought of, especially when he assumed they threatened her. Gon was not wrong about calling out their Moral Myopia.
Kite's death in the Chimera Ant arc, made even worse by Gon's complete denial of the possibility of his death, especially when it was obvious from the get go Kite had long since died and had been turned into a puppet by Pitou. The audience is painfully aware of this which makes Gon's complete breakdown at the Awful Truth all the more tragic.
Later on, he's technically revived as a Chimera Ant, but the person himself is still dead.
Chapters 274-275. "Killua. I'm doing the talking here." In a particularly heartbreaking case of OOC Is Serious Business, Gon brusquely tells Killua not to interfere while he's dealing with Pitou, and says it must be nice for Killua to remain so calm... "since this is of no concern to you". This is the same Killua who not very long ago had just managed to break free from Illumi's control for Gon's sake, and who had spent all this time at Gon's (his first and best friend) side; however (or because of it), those words are enough to break him. After Pitou manages to make a deal with Gon, Killua simply leaves the room without a word.
The events of chapters 304-307. Seeing the Kid Herobreak and give in to rage and despair is heart-wrenching.
What's worse is that after going on a Roaring Rampage of Revenge, he's completely broken both physically and mentally. In fact, he was nearly on his deathbed after fighting Pitou.
The easiest way to describe this fight is " no one wins". Despite Gon literally punching Pitou in half, the incredibly high cost to do so is absolutely horrific.
And meanwhile, Killua (who only manages to arrive after Pitou is already dead) can barely do more than watch in despair while all of this happens. Including when Pitou's body attacks again, and Killua pushes Gon out of the way, but Gon's arm still gets sliced off in the process... only for Gon to remain unnaturally calm about it, implying that he's become a Death Seeker. Killua has to watch his best friend break and almost die, and the only thing he can do is shout at him to stop.
The Chimera Ant King's death, especially with the pure black panels fitting his dying dialogue, which makes his death even sadder. It's almost a Japanese When the Wind Blows.
Alluka's Split Personality Nanika spends most of the time giving Alluka her Creepy Child cred. Then, after it's revealed that Nanika likes Killua enough to do whatever he says without any of the wish restrictions as long as it's a direct order, Killua tries to seal Alluka's power away by ordering Nanika to never come out again. Cue the creepy, blank-eyed Nanika breaking down and crying until she complies, and then Alluka angrily chastising Killua for making her cry until he agrees to take it back.
The final panels of the special chapters. If the entire annihilation of a clan wasn't enough alone, the horrible manner at which the Kurata were massacred is absolutely heartwrenching. Families were forced to sit, facing each other, as they were stabbed and beheaded one-by-one. Pureblood members of the Clan had their eyes gouged out. Children, wives, and husbands were tortured in front of their beloveds to illicit feelings of despair and rage from their victims in order to turn their eyes an even more startling shade of scarlet. This was the destruction of an entirely innocent race of people, at the hands of monsters.
Which makes Kurapica's quest for vengeance and Gon's outrage over the Phantom Troupe murdering people, even when they know full well how much it hurts to lose someone they care about, even more understandable and poignant. It also serves as a reminder that even though they have a tragic backstory of their own the Spiders are still a bunch of heartless, evil murderers when it all comes down to it, and there's no excuse for the horrible things they've done.
Speaking of the special chapters, the sheer contrast between the childKurapika used to be (not at all unlike Gon) and the personhe is now, also serves to drive home just how much of an impact the massacre has had on his life and his mental state, and how much he has lost from there. His return in the Zodiac arc a few chapters later doesn't help things. He has become extremely hostile and shut himself from his friends and everything, going from eagerly reading and dreaming about the outside to practically isolating himself in a dark room with the Scarlet Eyes he has collected, completely focused on his mission. Maybe, if the Kurata massacre had never happened and this were a different story, Kurapika could have easily been the hero of a more typical Shonen story. Instead, his revenge has become his only purpose and consumed everything in his life. It seems he has completely abandoned the promise he made to Pairo, which is deeply depressing.
The final ending for the 2011 anime homes this in. It's a heartwarming montage of where most the cast are now. Most are range from happy to bittersweet, the sole except Kurapika, who is still in a room staring at the eyes of his fallen clan. The final shots are of the main characters looking at the sun: Gon in amazement, Leorio sleeping on a desk, Killua with his sister... and a weary Kurapikain in an alley.
In a strange way, the Ant Queen's Death by Childbirth. It's immediately clear that despite the circumstances and the fact that most of her internal organs had been crushed during Meruem's premature birth, she still wishes him all the best and tells Colt to deliver him his name.
Killua's absolute breakdown at the feet of The newly transformed Palm. He's practically begging on his hands and knees for Palm to help and go see his friend (though he himself was half serious about that). His broken, anguished screaming as he's doing it doesn't help either.
Gyro's tragic backstory, how the only solace he had in his miserable life was the idea that deep down his father cared about and needed him, and how he completely broke when he found out both were false, and the resolve it inspired in him to make the rest of the world suffer. In spite of it having no payoff in the arc it's featured in and even in the greater story as of this writing (though it's flat out said that he and Gon will meet eventually, suggesting that he's a Chekhov's Gunman) it is frequently considered to be heartbreaking and a highlight of the arc's storytelling.