One of the things that pretty much can summarize the entire game from start to finish, is a constant string of these. It's difficult to get far in the game without running into these, and more often than not they chain together. The game's few Moments of Awesome often are also these as well. There are some specific to certain routes, and others that are encountered regardless of route.
Warning: As these will be drawing examples straight from the game and the given routes, there are obviously spoilers in abdundance. You have been warned!Tatsuki's Route
Tatsuki revealing that he's working on an airplane. The Heartwarming moment here is there he says that he made a promise to fix it so he could not only fly himself (something that, even as a dragon, he cannot do), but also fly Hiroyuki as well. It's implied he's been steadily working on this airplane in his spare time when not working on his dad for the last five years, just for Hiroyuki.
During the festival, Tatsuki winds up getting a little drunk again, but rather than just getting immediately frisky, he instead takes Hiroyuki aside away from the festival, where he confesses that he loves Hiroyuki, or at the very least, likes him very much. Considering how good of friends they've been during the entirety of the vacation, helping him work at his father's place by taking a part-time job there, the fact he's slightly inebriated doesn't tarnish the impact of his confession. The fact that Tatsuki's rather gentle with Hiroyuki on the first kiss despite his usual drunken behavior is impressive.
Picking the 2nd option I believe gives you the first sex scene, in which Tatsuki lets Hiroyuki top.
Doubling as an MoA, the second time Hiroyuki tries flying the airplane, and it works. While Hiroyuki's in it, Tatsuki asks him where he'd like Tatsuki to take him. Hiroyuki says he'd like to see the ocean beyond the mountain. And Tatsuki does just that.
During the get-together after the successful flight, Tatsuki takes Hiroyuki aside for a moment and tells him he wants to build a house for him. But that's not the Crowning moment, no, that happens when Tatsuki flat-out proposes to Hiroyuki right there by asking him if he'll live with him in the house he's going to build for him. All the while Tatsuki is trying to act stoic with a heavy blush on his face.
The night before Hiroyuki has to leave, Hiroyuki and Tatsuki go to a hillside to watch a meteor shower. After some discussion, Tatsuki starts to get a little amorous again. Hiroyuki immediately asks if Tatsuki has been drinking again. The answer? No. This leads into the second sex scene, which is in itself a crowning moment because of how gentle Tatsuki is, is also helped by the music which preceeds it (though the second scene itself is played in silence). Afterwards, they watch the meteor shower in each other's arms. It doesn't get much more romantic than that.
Kouya's concert, considering everything that has led up to this point, the climax of Kouya's storyline is extremely satisfying.
Running after and comforting Kouya after he reads the letter from his mother by the riverside, promising that you'll be his strength and shoulder some of his burden. There were implications earlier that Kouya has had a crush on you for a while which Kouya confirms later in the route, but given how often Kouya brings up this moment later in the route, this is heavily implied to be the moment that Kouya falls in love with you completely.
Kouya is a little annoyed that he and the Player got separated from the rest of the group during the Festival, to which the player comments that he had a lot of fun just being able to spend time with Kouya.
Kouya's emotional breakdown at the band practice, a couple days before his big concert. is a tear jerker no doubt, but the scene turns into one of these. The player consoles him again, like by the riverside, and Kouya realizes that he shouldn't shoulder the burden of his promise to his mother from the rest of his band, and the realization of just how burdened he is leads to him crying into your chest. You successfully get him to realize and confront what's bothering him, and it's obvious he's extremely touched. It also helps that this leads to your Relationship Upgrade later that night.
A smaller example is his bandmates' reactions. They didn't see Kouya's breakdown, since he left the room, but they figured out what had happened, but don't hassle him about it and comfort him over it the next day.
Fixing Shin's trust issues and the romance between you or Hiroyuki and Shin is one of the most heartwarming things in this game.
The going away party Shin throws for you the day before you leave at the end of the game. It's good to see the normally moody and distant Shin smiling and having fun with the rest of your friends.
Shin's goodbye kiss, where he kisses you in front of everyone, which shows how far he's come since you first arrived in town. Goes into Crowning Moment of Funny when he plays up the Funny Foreigner aspect of it to screw with the other friends' heads by pretending it's a Foreign Farewell.