Rika, seeing as she would travel to the Digital World for an unknown amount of time (and maybe never returning at all), dressing a very pink and very girly dress that she hates so much, just to make her mom happy.
Rika and Renamon rushing to take Impmon to the real world even when they had no time to waste (as the ship heading there would be out in minutes). Seriously, this could go on forever.
Rika, before rushing to the final battle, accepting a new shirt from her mother, with a blue non-broken heart (opposite to the blue broken heart she usually wore).
What makes it sweeter is that right after, her mother removes her own jacket to reveal her new shirt: one with a red heart. "We match..."
Rika's Character Development is completed in the Finale, when she cries for Renamon not to leave her, telling her that she loves her.
What about when Impmon tears himself away from his Tamers (who can finally share him and treat him as a friend) to go rescue the others, and Makoto gives him a toy gun "So you can go blast the bad guys" (the kid's like, 4). It then turns into a Crowning Moment Of Awesome when, while running in the direction of the battle, Impmon digivolves into Beelzemon, looks at the toy gun and it turns into a functioning arm-mountedBFG. There are fucking reasons why Beelzemon is this troper's favorite character from that series.
You know, Mako, this might just come in handier than you think!
That part is even sweeter. When Mako gave him the toy gun, Impmon was about to tell him it wouldn't help, but stopped himself to save his feelings.
Even after 10 years I watch that scene and it brings Manly Tears when he says "I've never felt this kind of power before, and this time I'm fighting for what's right!"
The fact that he fights so freaking hard to be The Atoner after realizing what he did was wrong is both heartwarming and sad in and of itself. His voice actor (both of them) really sell how complete and utterly desperate he is to make up for his wrongdoings.
Takato and Juri's conversation at night about him missing his parents.
Takato and Juri, period.
The good-luck charm Takato gets from his mother, as well as the note attached to it. It's pretty different in the dub, but both versions are incredibly touching to listen to.
In the beginning of episode 9, Takato is utterly afraid of Growlmon from seeing him fight Devidramon. Then you see tears from Growlmon crying out to Takato not to be afraid. At that moment Takato realizes Growlmon is no different from Guilmon.
Takato and Wargrowlmon at the end of episode 14 after beating Mihiramon.
Wargrowlmon: Takatomon... you are worthy Tamer. Thank you, for fighting by my side.
Takato: I didn't do anything, but trust you, and myself, I guess. (They both begin tearing up) Looks like we're gonna need a lot more peanut butter.
What is special is that Takato is hugging Wargrowlmon. While he is tiny, the affection behind the hug transcends size, allowing the hug to be as big as Wargrowlmon himself.
Everyone's reactions to Beelzemon's supposed death—Henry and Terriermon are completely shocked, Renamon quietly mourns him and calls him "a true friend", and Takato gets as angry as he did when Leomon was killed. Keep in mind, it's only been a little while since Beelzemon was trying to kill them.
And yeah, Takato gets angry, but this time he manages to keep it in check, so we also get to see how he's grown as a character which is kind of heartwarming in its own way too.
The fact that "Runaway Locomon" takes place after the series and shows that the kids and there Digimon are reunited. This is infact so heartwarming that the show's creators prefer to consider it canon.
Rika and Renamon's first biomerge, especially the buildup to it. The total devotion the pair of them have towards each other at that point is just overwhelming. Renamon tries to make Rika turn back because she doesn't want her to die, but Rika won't leave her side because she wants to protect her partner.
Beyond the show itself, the show itself had a Crowning moment of heartwarming when it helped an autistic child get better, as Steve Blum himself recounts (after the 29 minute mark).
All the kids reuniting with their families when they finally make it home from the digital world. It's done entirely without any sound and, for the most part, no animation, but it honestly doesn't need either.