The end of Chapter 1: Naegi doubts that Sayaka ever cared about him, after she attempted to frame him for a murder. Kirigiri shows up to assure him that Sayaka did care about him after all, although it's only a theory of hers. Naegi chooses to honor Sayaka's memory.
Kirigiri: ...Naegi-kun. There is one more thing I want to ask you...
Kirigiri: How did you know I wanted to talk to you about Maizono-san?
Naegi: Oh, that.
Naegi: I can read minds.
Naegi: 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 Yamada 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 Naegi from being executed and drops him into a garbage room, putting Naegi in a position to have 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 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, Naegi 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 Kirigiri shows up to 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 a 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, Naegi 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: Togami promised to kill the mastermind earlier, Hagakure decides to trust his instincts instead of his divinations, Kirigiri doesn't believe her father would have wanted her to sacrifice Naegi, and Genocider Syo 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. Hagakure, despite his role as comic relief, ends up saying some of the most inspiring things. Togami 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 Kirigiri, who cannot be touched until everyone else is roused.
In the If segment, 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, Hagakure 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 a Super High-School Level Baseball Player 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 Naegi 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.
Togami finally having a Throw the Dog a Bone moment towards Fukawa by actually praising her for doing a good job investigating.
In the anime, when they need to summon Syo to tell them about The Most Despair Inducing Event In History , Togami tells Fukawa "You're our only hope" instead of just expecting her to do it like he did in the game.
Oowada's and Ishimaru's friendship.
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 Naegi promise to protect Aoi in the case that something happen to her. It just goes to show that, despite how Sakura looks, she's a very devoted friend.
To some, the prelude to Celes' 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 Naegi 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 Kirigiri (the anime also adds up that she hands it down in a manner so Monokuma wouldn't notice) and face her death calmly. Even if Monokuma ruins her dramatic death, it's... kind of odd that to some, Celes probably still have some dignity in her spirit, that not even a Cruel and Unusual Death can diminish it.
The endings for Dangan Academy, especially for characters who don't make it to the end in the main game.