The moment when it is revealed that the slacker Reaper Koki Kariya is actually one of the most powerful Reapers, and passes up chances to advance in rank simply because he doesn't want a desk job. Even his boss fight is great, since he complains about having to fight the whole time.
Especially awesome if you get the joke of him calling the attack "Level i Flare". In Final Fantasy, Flare is a strong spell that shows its power in "Level x Flare". Keep in mind that "i" is used to represent imaginary units and then think how powerful that makes it.
The "level" part of the spell in this case doesn't represent its power, instead it means the spell targets all enemies with the level divisible by the number given. Which is still pretty cool in this context, what with him targeting and blowing up pretty much everything possible with it.
Level i flare is so immensely powerful because it hits enemies on every plane simultaneously, which is why it was even a threat to Joshua in the first place: he doesn't have all his godlike powers in the RG, so he would have been seriously hurt, if not killed.
And soon afterwards finding out why everyone says Joshua is a Jesus analogue.
"Here comes the Beat wagon!"
As far as I'm concerned, the attack Neku uses at the end of the final battle, where he fuses with all three of his partners and activates a giant skull attack, which finishes the final boss in one blow (and looks extremely cool while doing it) was probably the most awesome moment of the entire game.
In Solo Remix you instead do the max level fusion of all three characters that you have unlocked. which means depending on how you spent your Scarletite means you end up shooting the final boss with God Zilla Mr. Mew Eye Beams, Dropping the Moon on him, crashing a tidal wave on him, AND then finally finishing the boss off with the skull attack.
Joshua yelling "That's it, you are DONE!" and impaling a giant shadow rhinoceros with a beam of sacred light fueled by the souls of the dead.
Week 1 Day 7, Shiki fearlessly talking back to Higashizawa and stating that there's nothing he can do, she's getting back. Also a heartwarming moment.
Every player gets a personal one upon defeating Bonus Boss Panthera Cantus on Ultimate Difficulty. Don't pretend you don't feel all-powerful once you've finally managed to kick those kitten's asses.
The fact that Progfox does a Fusion by itself is awesome. There's no other instance of this anywhere else in the game.
All of the Level 3 Fusions are pretty awesome. Neku and Shiki ride a giant Mr. Mew that shoots two giant Eye Beams, Neku and Beat ride a tidal wave that crashes down onto the bad guys, and Neku and Joshua drop the freakin' moon onto the enemy.
The soundtrack. Tracks like "Twister" and "Three Minutes Clapping" do an amazing job to back up the style of this game.
Just before the fight with Anguis Cantus, all looks lost, but then... "Here comes the Beat Wagon!" Cue "Twister" playing in the background as Beat and Shiki pull their Big Damn Heroes moment!
A meta one for Square-Enix in the Solo-remix of the game. They managed to make the partner system much, much more useful and allowing the player to control it much more easily. Espically J's.
How about the part where you use the Rhyme pin to finish off Konishi for some sweet revenge. Even better in the Solo Remix where you can use the above object while at the same time beating Konishi down with Rhyme's brother, Beat.
You can actually attack Konishi with Beat in the original version, too. After hitting her with Rhyme, look at Beat's shadow. Konishi will stay up in the top screen for a second, during which you can attack her. Which means you hit her with Rhyme, sending her up to Beat, who pummels her back down, at which point you find her again and hit her with Rhyme, sending her up to Beat...