Hearing Eri's side of the story. The whole thing. "I'm nothing without her." and how she describes Shiki in much the same way Shiki described her ("She had (...) all the things I don't have.")
Neku calling Shiki by her name.
Shiki: When you see the real me...will we still be friends?
Neku: Of course.
The end of each week, seeing Neku so close to his partners, especially when you replay the whole game, are reminded of just how closed-off he was at the beginning, and realize just how far he's come by the end of the story.
The ending. The whole thing, particularly seeing Rhyme. And Shiki.
The World Begins With You.
The originally embittered Neku managing to win over Joshua with the Power of Trust? Definitely qualifies.
The end of the storyline in Another Day, seriously, it's hilarious but still honestly touching and cute.
Getting to battle Shuto at the end, and Neku's admission that he'd been hoping for that. And winning just feels really, really good.
Reading the last Secret Report. Hanekoma is talking to Neku - or, well, to you the player.
When Shiki discovers that she was Neku's second week entry fee — and promptly getting flustered upon figuring out what that implies. As a reminder... a Player's entry fee is whatever's most important to him/her.
The conversation about Kariya refusing promotions. Of course, ambitious Uzuki is infuriated about it, but...
It turns out that Rhyme's memories of him weren't her entrance fee. They were his entrance fee. Her relationship with him was the most important thing in his entire life.
Rhyme's entrance fee is another doozy. It is heavily implied that her fee was her own hopes and dreams. Sounds like a more self-focused fee initially, but one quickly remembers that she was trying to give Beat an example, help him find a dream to live for. In a way, the most important thing to Rhyme was being able to help her brother.
It's a small thing, but what about, in week three, Makoto's old boss trying earnestly to give Makoto good advice? Initially he plans to use Reaper Creeper, but throws it away, deciding that this is too important.
Another Day, while mostly hilarious, also gives you the fuzzies with its complete lack of real angst or danger. Everyone, even the villains, is just having fun by the end.
"You're not my "partner" anymore, man. You're my friend." One of Beat's lines during the endgame. It's a sweet enough sentiment when it's first said, but in the final sequence, the line is flashed back to, and this time given voice acting. The heartfelt, sincere way in which Beat says it is so powerful.
Beat has a good number of surprisingly touching lines. "Listen up Phones! Cause I ain't asking twice! Please... Help me... You gotta help me save Rhyme..."
As a meta example, the way the Anti Poop-Socking system as explained by the tutorial is simply awesome: it basically says, "if you're busy with school or work, this system has your back covered!". The example given by the tutorial is one that we all can relate to, as gamers, considering how often either school or work - or both - are likely to have prevented us to play games as much as we wished to at some point in our lives. The game essentially telling players that "it's cool if you focus on school, you can still come back later; we'll be waiting for you, and rewarding your efforts with some EXP for your pins" is simply touching, especially considering this comes from a game based on the concepts of life, death and afterlife. Amazing.
The icon for one of the sub menus on your phone menu is a picture of Beat and Rhyme bumping fists. Aww. Their relationship in general could count as an example, to be honest.
Meeting Sota and Nao-Nao, fellow Players, during Week 2. They are surprised to learn that this is not Neku's first playthrough, and even more surprised when they learn that his entry fee for this game was Shiki, his partner from the first. They are immediately very sympathetic and supportive, and pledge they'd play the game a million times over for each other. After Nao is erased, Sota's final words are for Neku and Joshua to rescue Shiki and live. The two might be Sickeningly Sweethearts, but they are downright genuinely nice.
The best part is how, right before they pledge to play the game over and over for each other and/or be the other's entry fee, they help Neku, who's blaming himself for the fact that Shiki didn't get to be brought back to because she's his entry fee, out his funk, telling him that it proves how much he cares for her, and that he shouldn't feel guilty about that.
It also kind of implies that, had Neku been chosen to be brought back instead of Shiki, he would have been her entry fee.
In the end, Neku's monologue to Joshua, wherever he is. It highlights how much he's changed. It's the longest fully voice-acted scene in the game, too, so you can really hear Neku's sincerity.
Same streets, same crowds too. Yeah, Shibuya hasnít changed a bit. But still, I donít think I can forgive you yet. You donít see it, but... those few weeks were very hard for me. Learning to trust people, having that trust broken... Finding out the town I pegged as small, and stifling, and empty... wasnít any of those things. Iím glad I met you guys. You made me... pick up on things I probably wouldíve just gone on ignoring. "Trust your partner." And I do. I canít forgive you, but I trust you. You took care of things, right? Otherwise, Shibuya would be gone... and my world with it. Hey, did I mention? Iíve got friends now! Weíre getting together for the first time in a week! See you there?