This is based on opinion. Please don't list it on a work's trope example list.
Tearjerker / Digimon Adventure 02
Ken's backstory. Considering the absolute bastard he was as the Emperor, it's amazing that most of the things Ken Ichijoji does afterwards can bring a tear to a viewer's eyes to the point it can be hard watching earlier episodes before his Heel–Face Turn. From his first recognizing his own Mother after coming out of a not-at-all-Heroic-BSOD, to seeing his dead brother in an illusion caused by his own desire to see himself punished for his misdeeds, to Davis yelling that he's not alone anymore while he's struggling with the serious mental and physical pain of trying to close a Gateway to the Dark Ocean that's haunted him since he was seven... This guy really had to earn his happy ending.
Wormmon's death. It's just downright heartbreaking.
The scene where Ken goes into the Digital Nursery and all the Digimon start whining whenever he comes near them and he finds Wormmon's baby form and holds it in his arms and starts bawling his eyes out.
The scene depicting Ken's relationship to his older brother. He both resented and admired Sam, an already hard position for a kid. And then, after the boys have a heated argument over the Digivice that came out of Sam's computer, Ken's finally pushed over the edge and in the heat of the moment, spitefully wishes his brother would just "disappear". And then tragedy strikes.
Props to the dub for not sugarcoating Ken's backstory and giving it the acting it deserved. Despite Never Say "Die" being in effect, it's painfully clear what happened to Sam and it is heartbreaking to listen to this story unfold.
Also his poor parents' (who've already lost one son and nearly completely lost another) reaction after he returned (briefly) to the Digital World and she thinks he's gone for good. Definitely Adult Fear.
Ken's parents acknowledging the mistakes they made in raising Sam and Ken and their tearful apology, and promise to be better parents, is equally painful and beautiful. Even more profound, considering that many kids in real life face similar circumstances.
The scene where Oikawa is harvesting the Dark Spore to inject it into kids he's tricked is hard to watch since we see Ken the closest to a total breakdown he had been at the point in the series since Wormmon's death.
Oikawa's backstory, (especially when he recalls when he was offered his Deal with the Deviland how, right before that, he's bawling in despair since his beloved friend Hiroki isn't there with him to see the Digital World they believed in as children.
BlackWarGreymon's Heroic Sacrifice to save Cody's grandfather after finally realizing the true meaning of friendship, WarGreymon sounded like he was about to cry.
Oikawa's death scene, where, for the first time since his possession by Myotismon, he wakes up long enough to see the Digital World finally. Then he finally gets to meet his partner Digimon just seconds before he dies, dissolving into energy and using that to heal the damage Myotismon did. Both Cody's plea for him to hang on, and his partner Digimon's line "Are you leaving now? But we've only just met!" are particularly effective.
Mummymon's Villainous Breakdown following Arukenimon's death at the hand of MaloMyotismon. It's hard to feel sorry for a villain, even if they are part of the resident Team Rocket squad, but to see his emotional meltdown and subsequent death as well makes you really feel sorry for him.
To compare, imagine James watching Jessie be tortured to death by Giovanni...after she hand-delivered him a Pokémon he wanted, and then being brutally murdered himself when he tries to avenge her. It's painful and heartbreaking.
Gomamon's torture from the episode Old Reliable and his weakened state afterwards is enough to bring any Gomamon fan to tears.
The fact that had Yolei not dropped her hand warmer, they may not have even FOUND Gomamon, who was unconscious from his injuries and buried in the snow. It's just lucky he's implied, by his later stages, to be an arctic-aquatic Digimon, meaning he could survive being buried under frozen water.
The illusion TK and Cody had, as their deepest desires are impossible to ever come true. Cody just wants to be with his dad and show him the Digital World, while TK wants his family reunited. While Kari and Ken got what they wanted eventually, Cody and TK have to cope with the fact that their own dreams couldn't be reality (although TK's parents are on civil terms, they don't seem to want to get remarried and live together like he wants).
Wormmon's image song, "The Future You Dreamed Of, The Future I Dreamed Of."
After Wizardmon's ghost comes back, Gatomon tries to touch his hand, but they can't, and they're visibly heartbroken over it as Wizardmon floats away. Then Gatomon thanks Wizardmon for the new life he allowed her to have and promises it wouldn't be in vain. Even the other DigiDestined are saddened by it, Kari moreso when she comforts her.
Her damn face when she realizes they can't touch hands. And Wizardmon's reaction? He looks at his hands, and with such a broken tone in his voice, can only say, "I'm sorry."
In the "Double Tamer" crossover, there's something extremely depressing about the fact that Daisuke believes that no one would care or miss him if he never went home. He is shown to legitimately believe that his teammates don't want him around and that he has absolutely no purpose on the team. Compounding this is that since the story is set between the Kaiser's fall and Ken becoming a Sixth Ranger, the audience could make the unpleasant leap that Ken might have succeeded in his suicidal attempt to destroy his former base since Daisuke wouldn't have been around to stop him and the rest of the kids might not have been bothered.