The reason Taiki will always help people in need is because when he was young it turns out a classmate ended up going to the hospital after he passed by and didn't help him, not knowing the boy was sick.
Almost anything dealing with Baalmon in the Sand Zone. HolyCow. To elaborate, we find out that he was part of a group of holy warriors, and that he had to kill them all, including his mentor Angemon, when they were mind controlled into attacking each other. When he finally discovers Lilithmon was behind it, he's mortally wounded himself, but manages to be reborn as Beelzebumon later... but not before Xros Heart fought a difficult battle and Baalmon took the bullet for Shoutmon and the others.
His lines as Reapmon as he's dying in Shoutmon X4's arms in the dub were just as heart wrenching.
Reapmon: Am I...Am I worthy? Have I become, a warrior?
Angemon: (appears in a vision and smiles) You are now a true warrior of the light my friend.
Reapmon: (sheds a tear) At last...thank you.
Then again later, when Beelzebumon sacrifices himself to stop Lillithmon in her Demon Beast form, stating that he will "always be watching over" Taiki. Made even harsher due to his budding relationship with Mervamon being cut short, and that he always considered his new life to be in Taiki's service.
Puppetmon's backstory in episode 20, thinking he'd been abandoned by his friends his faith in things like friendship and trust are nearly lost. A far more sympathetic character than the original Puppetmon from Adventure.
Even though he's just in the one episode, Grademon from episode 29. He starts out as a villain, is beaten by Xros Heart, and the Code Crown responds to Taiki's emotions and purifies the darkness from his body. Confused by this, he runs off only to show up later, committing an epic Heroic Sacrifice that ends up instrumental to Tactimon's defeat. His dialogue "I hate to do this to the new body you've given me... but it's the only weapon I have left!" and Taiki's Manly Tears of rage at Tactimon calling Grademon "trash"... gah. They made us care about a character who face-turned and sacrificed himself all in the space of one episode. Thankfully, he's amongst the Digimon revived in the final episode.
Episode 30, when Akari and Zenjirou are forced to stay behind in the human world. This later sets up a Crowning Moment of Heartwarming when they show up in the nick of time to pull Taiki out of despair in the second to last episode.
The death of Deckerdramon, where we learn just why Kiriha is so screwed up: He lost both his parents at a young age, and then had his family's fortune taken by his father's subordinates. At this point, Kiriha has been manipulated into attacking the others, due to his elaborate Social Darwinist philosophy... which itself is due to his own misunderstanding of his father's last words. Deckerdramon refuses to fight alongside Kiriha, and in exchange, the boy orders his digimon to attack him... but eventually, Deckerdramon gets through to him, and helps him understand his father's last words. But this is too late, as Deckerdramon is dealt a mortal wound - one that he could not have survived had he not been already injured. Deckerdramon dies saving them, leaving Kiriha to finally learn his lesson about the Power of Friendship... at a very deep, personal cost.
Damemon's death. We know he'll be back because he was confirmed to be in season seven, but after watching him slowly die from wounds suffered from a battle, and seeing Yuu, who previously believed digimon could not really die, crying for him not to leave him, really tugs at your heart. It all ends with a an Ironic Echo of Damemon's usually comedic Catchphrase: "Giving up is no good... no good..."
In that same episode, Apollomon's death. It strangely overlaps with a Crowning Moment of Awesome, due to Apollomon Fighting from the Inside against his dark side, the evil program Whispered, who is in control of his body... with the arm Apollomon himself had made lame in order to pay for the evil he'd been forced to do as a member of the Bagra Army. However, in the end, Apollomon dies with his people not knowing the truth about him, and celebrating the end of the reign of an "evil" king.
Speaking of episode 53, let's talk about when Shoutmon is killed fighting DarknessBaguramon. Made all the more saddening because he's the main digimon of the series, and the completeness of how it's done. Of course, we know he'll return, but the way it was presented hit so hard, and seeing Taiki, who'd weathered so many challenges up till now and kept his Heroic Resolve through it all, absolutely broken by it, made this troper cry Manly Tears.