The end of Chapter 1: Makoto doubts that Sayaka ever cared about him. After all, she had attempted to frame him for a murder. Kyoko shows up to assure him that Sayaka did care about him after all, although it's only a theory of hers. Makoto chooses to honor Sayaka's memory.
Kyoko: ...Makoto. There is one more thing I want to ask you... How did you know I wanted to talk to you about Sayaka?
Makoto: Oh, that.
Makoto: I can read minds.
Makoto: Iím just joking. I just have good intuition.
Alter Ego, full stop. A computer program built by Chihiro to help everyone in the event anything happened to Chihiro, the program is so sweet and friendly that Hifumi friggin' fell in love with it! And it dedicates itself to helping them all, in the spirit of friendship and his master, out of the same motives as it would if it were a real person, simply because they were all Chihiro's friends. D'aww...!
In fact, Alter Ego loves everyone so much that, in the "proper" way to end chapter 5, Alter Ego rescues Makoto from being executed and drops him into a garbage room, putting Makoto in a position to take free rein over the system, provided he can make it out.
The culprit in case 4 isn't a culprit! Sakura killed herself, just so all her friends would stop fighting.
In the same case, Monokuma tries to pull a "The Reason You Suck" Speech on Aoi Asahina, but for once the others declare the murder was Monokuma's fault for tricking Aoi with the fake note and they decide not to punish Aoi for accusing them all, just to honor Sakura's true "last request!" Aww!
After Chapter 5's trial, Makoto is stuck in a dump in the basement by himself. As you can expect, he's a bit down in the...yes. But frigid, anti-social Kyoko falls down the chute to bring him something to eat, keep him company, and help him escape, in repentance for her earlier pushing of the blame onto him. This is made no less adorable by the fact that she shows up with an empty ramen cup on her head. In fact, it kind of adds an odd charm to her.
In Chapter 6, the Big Bad, Junko Enoshima, offers everyone a deal: they can remain inside the school and safe from the apocalypse outside, if they're willing to execute Makoto Naegi. To save himself, Makoto must give them all hope by shouting at each of them, in turn, not to lose hope when they hesitate. Most of them have personal reasons for refusing to give up: Byakuya promised to kill the mastermind earlier, Yasuhiro decides to trust his instinct instead of his divinations, Kyoko doesn't believe her father would have wanted her to sacrifice Makoto, and Genocide Jill...well, she hates school life. What's Aoi's reason for not losing hope? She actually borrows one from the dead Sakura, because Sakura would say that to reach true insight, one must always tread a thorny path. Aoi decides to leave just because Sakura would want it that way! Aww!
Just the whole emotional climax of everyone regaining their hope, really. Yasuhiro, despite his role as comic relief, ends up saying some of the most inspiring things. Byakuya reaffirms himself as the heir of his family, vowing to rebuild it himself and make it reach new heights. And just finally getting through to Kyoko, who cannot be touched until everyone else is roused.
In the If alternate storyline, Leon, of all people, gives a Shut Up, Hannibal! to Monokuma for nearly driving Sayaka into further despair, and after that he admits that there's something he wanted to confess to Sayaka later, and it seems both mutually agree. Wow. If they're not, like, trying to murder each other, these two actually do care for each other.
Also in the same time, Yasuhiro is understandably pissed off that his crystal ball, the thing used by Leon to shut Monokuma up, was broken and it's gonna cost him a lifetime to recover that cost. Leon shuts him up too... by telling him that he'll buy that with the money he'll win via baseball tournaments. Yes, not only he tells that, he pretty much embraces his status as the Ultimate Baseball Star instead of trying to leave that to chase girls. It's kinda telling that he would be a Jerk with a Heart of Gold if he could hold on a little longer.
Then there's his arc in Dangan Academy. In Leon's ending, after Makoto tells him it's okay to do what he wants and not to bottle up his doubts for fear of looking uncool, he decides he'll go back to playing baseball but keep working on his singing—once he's finished his athletic career, he'll still have a dream to pursue.
In episode two of the anime, as everyone leaves to commence the investigation, Mondo strips off his coat and lays it over Junko/Mukuro's dead body. It's oddly touching.
Byakuya finally having a Throw the Dog a Bone moment towards Toko by actually praising her for doing a good job investigating.
When they need to summon Syo to tell them about The Most Despair Inducing Event In History , Byakuya tells Toko "You're the only one we can rely on now" instead of just expecting her to do it.
Aoi Asahina and Sakura Oogami's friendship in general is incredibly heartwarming. Sakura is incredibly threatening and strong (to the point of being nicknamed "Ogre" by some), and Aoi is cute and energetic. They bond over their love of personal fitness and are often seen together. Aoi calls Sakura a cutesy "Sakura-chan" and is constantly going on about how strong and impressive Sakura is. In turn, Sakura is extremely protective of Aoi, threatening anyone who upsets her and staying by her when she's afraid. Also, in one scene, Sakura promises to believe Aoi no matter what happens. Sakura also makes Makoto promise to protect Aoi in the case that something happen to her. It just goes to show that, despite how Sakura looks (and despite her role), she's a very devoted friend.
To some, the prelude to Celeste's execution. She has a clear case of Lack of Empathy. And with her pissy attitude and true personality revealed, she's in a perfect and plausible position to scream off in anger that her plan was ultimately ruined and cursing Makoto and the others at her demise (and it'd be in-character too). She doesn't. In fact, she stayed calm, admits her crime, gives the key to the locker where she locked Alter Ego to Kyoko (the anime also adds up that she hands it down in a manner so Monokuma wouldn't notice) and faces her death calmly. Even if Monokuma ruins her dramatic death, it's... kind of odd that to some, Celeste probably still have some dignity in her spirit, that not even a Cruel and Unusual Death can diminish it.
In her parting words to the group, she hopes that maybe they'll meet again in another life. This becomes both more heartwarming and Harsher in Hindsight when The Reveal about characters' memories being tampered with comes up, with photographs showing that before her memories were altered, Celestia was good friends with the other students.
The endings for Dangan Academy, especially for characters who don't make it to the end in the main game.
Not only the endings, but the gameplay progress as well for those who not only did not make it at the end, but ended up being portrayed as unsympathetic, just to show that they're all perfectly sane and genuine friends when they're not being pushed to their limits. We already mentioned Leon's deal before, now Sayaka can afford to be the genuinely sweet girl that she displayed herself before things went south, while Celeste, even if she's still a highly condescending girl, no longer sees the need to murder everyone just for her selfish dream and even permits Makoto to pursue it with her as a B-Rank Knight. In other words, the Academy works it way to show that they're not that unsympathetic as the main game portrayed them to be at their end.
Makoto paying his Due to the Dead in Chapter 6, when everyone else just saw Mukuro as either the mastermind or the mastermind's lackey. Even without his memories, Makoto is still the only one that treats her kindly.
Kyoko's eyes going wide when Makoto calls her a friend. It says a lot that someone could become so jaded to deception that it takes honesty to catch them off-guard.
In the If alternate storyline, Mukuro and Makoto's friendship throughout the story is all kinds of heartwarming, with the former secretly being in love with the latter.
After Makoto ends up Taking the Bullet for Mukuro, Makoto gives Mukuro a smile after seeing that his friend was unharmed, despite being in agonizing pain from having a spear impaled in his abdomen.
When Monokuma tried to manipulate the other students to attack Mukuro and Makoto, Mukuro put Makoto safety above her own by trying to convince the students that Makoto was innocent, although she was unsuccessful.
Their reunion in the cafeteria after Makoto's (partial) recovery from his injury.