Plus, the way Soren shows his softer side around Ike, showing concern and compassion when such things are normally not his specialty. Their entire support set in Path of Radiance is pretty heartwarning.
Elincia reuniting with Geoffrey, Lucia and Bastian is just so adorable, especially considering she thought they were dead and nope, not only are they not dead, they're ready to kick ass and take names for her!
In RD, Leanne trying to save Naesala from Skrimir just made me say "Awwwwwwwww!" Of course he steps in and makes sure she doesn't get mauled, but still.
Mist and Jill's entire support set, from Mist adamantly reaching out to a depressed Jill to the two of them crying in each other's arms. Especially if you get them to A rank after chapter 20:
Jill: Mist... You make all of my worries go away when you're near me...
Jill: The world is hard. Hard and cold and... terrible. Even so, you make me... You make me want to keep going
Not heartwarming so much as incredibly adorable, but when Ike complains to Volke that the latter never shows up for dinner while they're sailing to Begnion, he clarifies that Mist is thereby convinced Volke is not getting anything to eat and has been repeatedly wandering around the ship looking for him carrying a plate of food. Go on. Picture Mist doing that, possibly calling Volke's name like she's searching for an antisocial cat.
Ike and Elincia's friendship. Ship Tease aside, she places her trust in him and he believes in her so much. And then there's the ending cutscene.
Gatrie reuniting with the Greil Mercenaries in chapter 13, if you have everyone talk to him before he's recruited. He even feels bad for leaving after Greil died, but Ike tells him it's nothing to worry about.
Lethe asking Jill to shake her hand in their A support, after the latter shows she finally understands why her previous view of the Laguz was wrong.
Ike and Mist's relationship, especially after the death of their father. Such devoted siblings.
If Oscar, Boyd or Rolf visits a certain house in chapter 3-1 of Radiant Dawn, you'll unlock a special base conversation in the following chapter between the woman there and the three brothers. The woman is actually Rolf's biological mother trying to make ammends, but Boyd calls her out angrily for abandoning the family, while Oscar asks Rolf if he'd like to talk to her. Rolf declines, saying that his brothers and the Greil Mercenaries are his family and telling Boyd he loves him no matter how much they argue.
Rolf's great concern and care for Mist after the death of Greil in Path of Radiance, especially in his base conversation with Ike in chapter 8. Their A support is pretty sweet, too, with Rolf crying to Mist that he knows the war isn't a game, he's just afraid if he doesn't fight like a big tough guy he's going to lose everyone he loves to the enemy.
The heavy-on-fanfare Mist/Boyd supports from Po R and the ending in RD: In Po R, what starts off as a hatred of sorts eventually turns into Mist bawling her eyes out into Boyd's arms, who tells her everything will be okay, even if he "has no idea what he's doing". In RD, when Mist faints from the war and the medallion in the Part III Epilogue, Boyd clears a path so Ike can take Mist to safety if they have the A Support. Just before that, Mist yelled at Boyd for trying to stop her from fighting- again only if they have the A Support. In their ending, they get married, and much to Boyd's dismay, Mist cries during their wedding vows.
The "Master and Pupil" base conversation in Radiant Dawn. Awww...
Shinon and Rolf in general, really. The fact that Shinon is a total Jerk Ass makes his kindness towards the boy all the more special.
Near the ending of Path of Radiance, Ike tells Nasir that he never stopped trusting him, not even after finding out he was The Mole. Nasir makes a Call Back to their conversation on the boat about how war would change Ike by saying that not only did Ike stay true to himself, he helped Nasir believe in things like idealism again, and tells him to never change.
Before that, there was Nasir's conversation with Mist after The Reveal that he stole the medallion.. It pretty much comes down to him apologizing profusely and Mist accepting it without even hearing the reason why he did so, because he's her friend.
The supports may have been nerfed in Radiant Dawn, but sometimes you get lucky and get lines like this:
Sanaki: [Reyson,] remember that Begnion stands with you.
Reyson: Tibarn, I...owe you my life. You took me in, made me a part of your family... I owe you so much. No matter what happens in this war, I will stay by your side, be it in body or in spirit.
Soren's other special scene at the end of Radiant Dawn deserves mention too, specifically Almedha's reaction to meeting him.
Almedha:Because I have lost the power of my birthright, I thought... Maybe I wouldn't be able to...That I might not be able to recognize my own child. But when her own true son stands before her, no mother could fail to know. Oh, my son, you've lived and grown strong.
"We are all family. We will try to understand one another. Even when we disagree."
Also in Path of Radiance when Sanaki got down on her knees and begged the herons to forgive her and her country for what they did to them... and they did.
Sothe and Micaiah. Radiant Dawn. "I'll protect you." Enough said.
Ike and Ashera/Yune/Ashunera's final conversation in Radiant Dawn. "Because if we don't have that, we're nothing more than... statues...
Geoffrey's dialogue with his sister Lucia and his love interest, Elincia from Path of Radiance/Radiant Dawn also qualifies. The part where he tells Elincia that if he died, he could at least die near her? Elincia's response: "Please...never leave my side, Geoffrey."
Ranulf in his Path of Radiance A-support with Ike says he trusts him as much as any beorc, but it's different since he's not a fellow laguz. And if you likewise get them to A-rank in Radiant Dawn... Ranulf leaves Tellius with Ike, unlikely to see his country and people again. And you know Ranulf, he loves Gallia and all its citizens, and has a respectable position as the king's right hand. But for Ike he leaves the entire life he's ever known behind; and he's OKAY with it. That the one he comes to trust the most of all turns out to be a beorc is really amazing.