A minor one, but this is what Riki can say to Melia when her tension is low:
"Melly, want hug?"
It is probably safe to say that Fiora and Shulk are a major source of this in the game. Particularly, anything and everything on the Fallen Arm. Over and above the above examples, we have:
Shulk and Fiora have unique dialogue when healing each other in battle.
The Heart-to-Heart "Just Like Old Times", wherein Fiora pours out her heart regarding worries about being together with Shulk because of her Machina body, because she doesn't want people to look badly at Shulk. Shulk retorts that he doesn't care what other people think, as long as he can be with Fiora. He makes it fairly clear that no matter what, his overriding goal is, always has been, and always will be Fiora.
Linada stating that she, with what she has here, can't possibly restore Fiora's homs body, and Fiora responding that she doesn't care as long as she can be with and protect Shulk, which leads into...
Shulk's got a lot of internal dialogue when he checks on the unconscious Fiora, but most sweetly is something he never expected to be able to say after the Colony 9 attack: "Goodnight Fiora, I'll see you in the morning". You can practically feel the smile on his face. Then, a minute later, you get to see the smile on his face while he sits next to her just before her surgery.
Their post-battle banter when they're the only two in the party, particularly when they're alone on the Fallen Arm.
Fiora's final skill tree being entirely devoted to buffs she gets from Shulk being in the active party. It is all unique to her so you cannot link them with other party members. It is both kind of funny and super-sweet.
Reyn opens up to Sharla that he's feeling unneeded now that Shulk is strong enough to protect himself. Sharla returns the favor by encouraging him to treat Shulk as an ally whose back needs guarding instead of someone needing protection—exactly what Reyn needs to hear, and sure enough he and Sharla pull a Big Damn Heroes moment not five minutes later.
Dunban asks Melia how she's doing and she replies that she's fine, but Riki insists to make camp since he's tired and hungry. Gilligan Cut to the three around a campfire with Melia in a very deep sleep and Riki catching fish. Dunban quickly figures out that Riki knew just how tired Melia was, even though she wouldn't admit it.
On that note, the entire conversation between Riki and Dunban right after that scene, the most unlikely Odd Friendship in the game, as they bond over their parenting experiences. The absolutely lovely music box rendition of Riki's theme that plays during that moment seals the deal.
And one more for Dunban, when he finally reunites with his little sister. Definitive Edition adds even more to the scene - Fiora mentioned earlier that Dunban is too proud to cry in front of anyone. The added visual fidelity makes it clear it takes everything Dunban has not to burst into tears in this moment.
Fiora: Dear brother...
The Machina of the hidden village welcoming Shulk and co. with open arms, even if they are initially suspicious of these "people of Mechonis".
For Melia, Kallian's death and his last words. Also doubles as a Tear Jerker due to the beautiful music. Melia nearly breaks down when Riki confirms he also heard Kallian's parting words to her.
The Heart-to-Heart "Eternal Scars" at the Black Wreckage. Even after everything he did, Dunban still mourns Mumkhar's death and wishes him peace.
The final one between Shulk and Riki, where Shulk laments how he doesn't have a family waiting for him back home after their adventure's over. Riki's immediate response? Tell Shulk if he wants him to be his daddypon and become part of his family.
Shulk: ...Wh-what was that, Riki?! Riki: Shulk can live with Riki and Oka, then Shulk have family waiting! Shulk never get sad again! Shulk: ... Riki: Shulk not like Riki's idea? Riki very, very sorry, Shulk. Riki only want to see Shulk happy... Shulk: No, it's not that... Thank you, Riki. Thank you so much. No one's ever asked me to be a part of their family... Riki: Shulk not worry anymore! Riki want to always see big Hom Hom smile from ear to ear! Shulk: (You are a great friend, Riki...)
Restoring Colony 6 and sending more immigrants to live there brings warms feelings seeing all sorts of different species coming together. Not to mention the fact that the colony's theme becomes more and more livelier as you do so.
Berryjammy's life does indeed improve when she's migrated to Colony 6 due to the fact that the people there don't mock her name (unlike within Frontier Village, where the locals did just that).
If you revisit Colony 9's Weapon Development Lab at a very late point in the game while playing as Shulk, you'll get the quest "A Token of Friendship", where Shulk wants to use all his new-found experience and expertise to make the best weapon he can for Reyn. It shows that, even after all they've been through and all the people they've met, Shulk and Reyn's bond has remained extremely strong, and it's heartwarming to see Shulk want to do something nice for Reyn.
During the "Melancholy Tyrea" sidequest, Tyrea insults Melia's bloodline and legitimacy to the throne. In response, Reyn calls Tyrea out and delivers an inspirational speech defending Melia's honor. Contrast that with Reyn and Melia's initial impressions of each other ("This large one is far worse." vs. "I'm not good with her posh accent"). It's touching to see just how much their relationship improved throughout the journey.
Reyn: You don't have the faintest idea why Melia's been fighting. Even if you'd been born in her place, the Emperor still would have chosen her as his successor. Succeeding the imperial line ain't all about blood. It's about takin' on the will to do whatever it takes for your land, for your people, when the time comes. That's what makes Melia different from you!
A Mass-Produced Faced Mechon saving Juju from the Telethia at the end of the game, followed by a confirmation that the Mechon are now on the side of the heroes. What sells the moment is the fact that Mass-Produced Faces look just like Xord. A version of the Mechon that destroyed Colony 6 now is protecting it from Telethia. Even better the song that played when Xord captures Juju plays in that scene as well. Doubles as a Moment of Awesome.
The Streetpass Mii Plaza game "Puzzle Swap" has a puzzle panel for this game. Normally, it depicts Riki and two other Nopon (his children, perhaps?) playing around the Monado. Then you pan to the right to see Shulk and Fiora, gazing up at the Mechonis in the distance together.
In one of the Quiet Moments, Melia taking to heart what she and Nene had talked about previously regarding sisters, and telling Tyrea that she's the only family she has left and that this is one reason she wants Tyrea to join her circle of comrades and stick with her as she takes on her duties in Alcamoth. Tyrea is visibly touched, even if she is unwilling to commit to anything yet.
Kino at one point says that he's always thought the Heropon's main role is to make a ton of friends, rather than monster-fighting duty. Why exactly? Because despite being a war hero and saviour who's traveled the entire known world and defeated all kinds of powerful foes, the only thing Riki ever brags about is all the friends he's made during the quest.
After all the crap the High Entia went through in the main game, Future Connected gives them a hopeful future.
The Telethia are no longer a force of malice and instead help the party out numerous times, heavily implied to be regaining their High Entian identities.
Teelan, a boy from a sidequest where you help him find Telethia research, is actively researching for a way to save the pureblooded High Entia from their transformations.
Tyrea is not only helping Teelan with this research, but also makes amends with Melia and becomes her "shadow": providing her with support in her royal duties.
Alcamoth is reclaimed. And with the help of Colony 9 in conjunction with the Bionis' Shoulder population, they manage to rebuild the capital and the game ends with Melia's coronation.