"Trash Day" Gabumon promising that he'd stand by Matt, no matter what. The crest of friendship's glow is restored, and he Warp-Digivolves to MetalGarurumon. Doubles as a Moment Of Awesome as well.
"Sora's Crest of Love" is pretty much an entire episode of this. We find out that while the group was separated, Sora and Biyomon had been helping them all along. Sora figures out her mother really did care about her when she feels the same way about Biyomon, her love for her partner ultimately triggering her crest to let her digivolve into Garudamon.
When Sora is refusing to admit that she can love, TK proves that Children Are Innocent after all. He asks Sora not to go away again because he missed her and that when she's around he doesn't miss his mother so much. Sora is moved to tears by this, realising how silly she has been.
TK's words are a bit more of a Tear Jerker in the sub as he tells her that he wishes she'd stay because he doesn't like when his family- er, the team is separated.
It's a minor thing, but Koromon and Kari playing pattycake together in episode 21 is just too adorable not to mention.
Even after everything that happened in the Princess Mimi episode...when the Geckomon and Otamamon see Mimi again, they're so THRILLED TO SEE HER! It was just so cute!
Joe, Mimi, Palmon and Gomamon striking up a friendship with their old foe Ogremon was just so sweet as well.
After Kari got sick, and spent a while separated from her brother...Tai has been worried sick about her, and they're finally reunited again, what do they do? Run to each other, Tai picks his sister up and twirls her around! Everyone with me now...D'AWWWWW!
Tai barreling in to save Sora from Datamon always brings warm fuzzies to my heart!
Just the simple act of Matt going through all the trouble to take TK home who lives far away now is so sweet. Heck, any small moment where you see Matt and TK show that they care a lot about each other is just so sweet.
Patamon: "We like it when you guys get mushy."
Kari freeing a large group of Numemon from slavery, and the Numemon trying to save her life in turn.
Perhaps the Most powerful Moment of Heartwarming, in this tropers opinion, was from Episode 37. While doubling as a Tear Jerker, it is Wizard's last words before dying after Myotismon's Grizzly Wing attack. He tells Gatomon/Tailmon that she doesn't need to apologize because he had no regrets for making his sacrifice to save her. Then on top of that he thanked her for befriending him so that he wouldn't have to live aloneforever in misery and thus giving his life meaning.
In episode 14 we see the Yokomon from episode 4 arriving to help the Digidestined build a raft. Biyomon reuniting with and hugging all her 'sisters' is just so darn adorable.
Mimi apologizing for her brattiness is "Princess Karaoke'', and the others forgiving her.
During the introduction of the Dark Masters, there's a brief shot of Angewomon being knocked out of the sky and Kari running to try and catch her. She gets bowled over, of course, since Angewomon is about three times her size. It's very adorable.
The surprisingly fantastic Digimon movie shows Tai and Matt travelling into the internet, not with Techno Babble, but through sheer love for their Digimon.
Tai: "Listen, I don't have a whistle to wake you, but I want you to know you're not alone. Okay? And the mail keeps coming. It won't stop! Kids from all over the world are writing to you. They need your help. You're the only one who can do it! Feel their hope! Feel their strength!"
The sequel Diaboromon Strikes Back, has another moment on the part of a crowd of nameless onlookers. Diaboromon has appeared in the harbour a la Godzilla and pretty much half the city has shown up to watch the fight, Omnimon is out for the count and things are looking pretty much hopeless, when Ken and Daisuke show up and hear their Digimon calling for them across the crowded peer. They struggle to get to each other through the throng of people — then Daisuke yells and the crowd, realising who (and what) these two kids are immediately part en masse to let them through and reach their partners - all of them smiling, cheering and encouraging them.