Sazh and Dajh. During the fireworks festival that the whole party was at, Dajh is wishing on the fireworks for Sazh to be happy since he doesn't smile anymore. This immediately makes Sazh hug Dajh and tells him that his wish came true with a smile and as he stands with Dajh on his shoulders and when asked what he's wishing for, Sazh says that's his little secret.
Hope's father. "You're my son! This is your home!"
Shortly before that, the normally icy Lightning seeing Hope's distress and sweeping him up in a hug, then helping Fang scoop up Snow and saying affectionately "He's too stubborn to die,", making it clear that she cares.
What makes it better is if you remember that she said the same thing about him before, but more ruefully.
In fact, Bartholomew's view of the I'Cie 'fugitives'. While it's understandable he wouldn't see his son as a supposed 'monster', he didn't know the other three at all, and yet he treats them exactly as he would other humans. Even Snow, the one indirectly responsible for Nora's death, who he'd have good reason to be angry at. But no, never once does he show suspicion or hostitily toward them. For someone living in a society where anything Pulse-related is meant to be feared/hated/destroyed, that's quite heartwarming.
And this is coming shortly after the mob scene that quite clearly illustrated the rampant paranoia associated with Pulse I'Cie, making it ever better that Bartholomew shows nothing of the sort.
He shows a great deal of So Proud of You, sternly correcting Hope's anxiety whenever it crops up. "You're not running! This is not running away. You've made a choice. You'll survive, and do what needs to be done."
Lightning restoring Snow's faith that Serah can, and will, be saved.
Speaking of Snow and Lightning, the conversation they have about what they'll do when Serah's no longer crystal. Seeing Lightning soften up is pretty poignant. Especially when, as the scene fades out, you see her rest her head on Snow's back.
From that same scene, Snow telling Lightning exactly what she needed to hear. A possible interpretation of her bitterness towards Snow is that she feels that she is losing Serah to him. He only needs one line to reassure her that she is not. It's at that moment that a silently crying Lightning looks up, takes a step towards Snow and rests her head on his back. She believes him.
Snow: Don't worry. We'll finish this... and go see her together.
The exact moment when Lightning realized that she was being an Aloof Big Sister when she realized that Snow was the only one who stood by Serah when she became an l'Cie.
XIII is really just full of them. Fang and Vanille, Lightning and Snow, Lightning and Hope, Hope and Snow, Vanille and Sazh. Really, every other cutscene is gonna have some touching dialog.
The Snow and Hope conflict. Snow's absolute refusal to leave Hope and his determination to protect him even after Hope tries to kill him to make up for the past.
Hope: You wanna die? Well, too bad. You can't!
Battle Team Change | IN-> Hope: Ravager
Hope: I won't let you!
Snow: "Serah... my one, my only... will you marry me?"
His reaction after Serah answers him is equal parts Funny and Heartwarming:
"She said yes!"
After Vanille's Eidolon battle, where Fang tears into her about how she is the one person Vanille shouldn't have lied to, given all they've been through together. She rears back to punch Vanille and ends up just bopping her lightly before reminding her that they are family.
The ending, period.
Hope and Vanille's scene on Gran Pulse. Him joking about having feelings for Vanille, and her cute reaction...so adorable!
The scene where Snow decides help Serah fulfill her focus instead of abandoning her is all kinds of sweet. He's literally saying he'll take on the entire world just for her.
In the end, Snowsteals a moment away from Serah and Lightning, and talks about planning the wedding. He tells Lightning, "I will make her happy." Lightning's response is a simple "I know." D'aww, Light, you weren't so icy after all, were you?
Just before Snow makes his awesome entry with Fang. Lighting and Hope are completely surrounded, and Lightning tells Hope to run while she holds them off. "You survive."
Despite his justifiable anger at Vanille, who was more than willing to take the blame and get killed in retribution, Sazh can't find it in himself to hate her, much less shoot her.
"Lot of things can be excused. Shooting kids ain't one of them."
Which is followed by Vanille's:
"Kindness like his, you don't forget."
Snow's devotion to Serah throughout the whole game.
After a tear-inducing scene in Nautilus, wherein Sazh confronts Vanille about her lies, Brynhildr appears and readies her scythe to strike Sazh - who is willing to die at this point - down. Vanille quickly places herself between them and stares the summon down, turns her head to Sazh, and says "It's not over."
Sazh moving to protect Vanille when Brynhildr gets ready to shoot her is also very heartwarming, given what he has just learnt about her.
It's easy to miss and only a minor heartwarmer, but when exploring the world with a party, if all three members stop moving and are standing close to each other; pan the camera around to the leader. He/she will give their teammates a reassuring smile.
It's a little thing, but the way that Lightning says "Hope?!" in battle and his HP goes critical.