Frankly, after the sheer ambiguity the series has put forth in this position, this line was long overdue:
Sora: No. Roxas, you're you, we're not the same. I wanted to tell you that. That you deserve, just as much as I do, to be your own person.
Roxas' response is just as awesome
Roxas: Sora, see? That's why it has to be you.
Translation: "You're the one who has to live and fight for the both of us, because you care so much for others." That's right, Roxas is willingly acknowledging that Sora is a better person than he is. It takes some guts to do that, especially in his situation.
Riku's retort to Ansem's claim about Riku needing to learn to embrace darkness or risk death. His response is to draw his Keyblade and declare that he walks the road to dawn and once Ansem leaves, Riku proclaims that as long as he has a Keyblade, he'll be fine.
There's a subtle one in Riku's final final boss fight. As his desperation attack, the boss readies a ShotLock, which is a bit of an Uh-Oh, since Riku doesn't have anything readily available in his arsenal to take that on note His best magic or his Spirit Links weren't anywhere near as powerful as the shotlock Limit Breaks. However, Riku falls back on his Dream Eaters, who give him enough of a generic boost in power that he's able to meet the boss's Limit Break head on with sheer force. Even better the if you pay close attention the attack he's using is his signature move Dark Aura. That's right, one of his moves in the first game is used to beat a Shotlock.
Sora's final boss fight— Xemnas—showcases just how badass he is. First of all, Sora's been kicked back into his fourteen year old body, so he's well below his peak. Second, Sora is essentially in the Realm of Darkness, or somewhere of comparable darkness, so he's being constantly eaten away and corrupted. Nevertheless he's able to beat down Xemnas, who could have made mincemeat of Sora when he was fourteen, and whom Sora was barely able to beat even with Riku's help in Kingdom Hearts II. And it isn't until after the battle is over that Sora collapses and gives in to the Darkness. And this is with Xemnas pulling out all the stops—warping the Arena, throwing lots of skyscrapers, and attacking faster than in his other fights in the series.
The opening CG sequence of the game is a quick, but very impressive, recap of the main points of the series so far. The main point of attraction though, is the final scene which appears to actually foreshadow both III AND χ; Mickey uses magic from a spellbook that launches several glowing pages from it; the pages then transform into Terra, Ventus, Aqua, Roxas, Donald and Goofy. They all land together, in front of Master Xehanort, with Sora leading the assault for the implied final battle.
Also, keep in mind that this all can be viewed in full 3D.
The cherry on top though is that on the bottom screen, until the aforementioned foreshadowing, a silhouette of Mickey is seen conducting the music/events a la Fantasia. Oh, and he's reacting to what's happening on the top screen, until finally jumping up there to help out!
Also, there's another awesome moment lifted straight from the original movie. Remember that one time, when Frollo, about to kill Quasimodo with his sword, fell to his death instead when the gargoyle he was standing on cracked itself on purpose? Well, guess what? That scene actually made it into the game! Of course, given the Glowing Eyes of Doom were already scary the first time, the fact the scene is now in 3D may or may not detract from the awesomeness of the scene.
On a meta level, the game itself got one when it reportedly "reached the expected number of sales within four hours".
The World That Never Was has been revealed to be the ruined one following the climax of KH2; when Sora confronts Xemnas and Xigbar there, he repeats his "my friends are my power" line... causing Xemnas and Xigbar to freak out as a vision of Sora, Riku, Kairi, Mickey, Donald, Goofy, Terra, Ventus, Aqua, Roxas and Xion appears before them. Before the video inevitably gets pulled from Youtube you can see it here.
The whole scene counts because it's basically a Wham Episode of big proportions that mocks one of the big Aesops in the series, and then proceeds to show exactly why it is so powerful and useful, topped of with one of the best uses of the "my friends are my power" line in a KH game. What basically happens is that near the end of Sora's story, Sora catches up to Riku and Kairi, only to see them transform into Terra and Aqua, and himself into Ven. This confuses him and makes him recall the time when Aqua visited him and Riku when they were kids. Suddently, Ansem SoD appears in the dream, and he eventually finds himself back on a path of buildings, together with Xigbar who explains that everything he saw was a dream, and that Xigbar put him to sleep. Xigbar asks Sora about how his heart felt by experiencing them, to which Sora says that he felt painful, and that it made him chase the dreams. Xigbar reveals that by chasing the dreams, Sora's heart made sure that Sora himself have practically fallen into their (read: New Organization XIII's) clutches. Sora retorts that Xigbar and the rest of the Nobodies must have had hearts themselves, because he felt both Roxas', Xion's, and Axel's tears. At that point, Xemnas (who has antagonized Sora throughout the game) appears and confirms this. When asked why the Organization were lied to, Xigbar proceeds to reveal that the Organization were not created to give the Nobodies new hearts, but to plant part of Xehanort's heart into all of them, turning them into Xehanort. When asked why he would agree to something like that, Xigbar quips that he is already half Xehanort himself! Xemnas proceeds to go on about how most of the people that were chosen by the Organization, weren't fit for it, and that they instead used them and their budding hearts to achieve other goals. This pisses of Sora who replies that the heart isn't a plaything for them, and that his friends' hearts are what gives him power. This prompts Xigbar to mock him, stating that because Sora's power comes from others, he himself is virtually a zero and a nobody on his own, before saying that there's no way that the Keyblade would have chosen him had he not been connected to others who do. Sora then proceeds to say that even if it wouldn't have chosen him on it's own, he is still happy to be part of something bigger, and this is what causes the vision of almost every protagonist in the series to appear beside him, freaking Xigbar and Xemnas out. After being played for a fool by the new Organization for almost the whole game, he manages to make them freak out at the time where they were at their most triumphant, and it is awesome!
It finds itself on the Heartwarming page for this game as well, but when Young Master Xehanort shatters Sora's Heart, Ven is the one who rescues him, giving him his armour and shielding his body. This is impressive seeing as just before this, Ven was comatose for at least a decade.
Just when Master Xehanort is about to blast Sora to oblivion, Lea saves Sora at the LAST second!
Lea gains a Keyblade at the game's end. THAT is all.
It's the way he gets it too - it pops into his hand and he's just like, 'Oh, there it is', while everyone else freaks out because none of them expected him to be able to summon one.
How about the fact that even Yen Sid didn't even see it coming? He's just as surprised as everyone else, likely including the player!
In a meta sense, the fact that he went from a minor villain character who was supposed to die at the beginning of 2 to a main character who saves the heroes multiple times and even earns a Keyblade through sheer stubbornness is a big one for Axel/Lea.
The Secret Ending implies that Kairi will have more action next game.
Implies nothing; the subtitles for the scene outright say that she is the seventh and final Keyblade hero meant to fight against Xehanort. The most awesome part of this moment is The Reveal that it is Kairi who is even there, panning up to her with a badass look on her face that makes her greatly resemble Aqua, if it wasn't obvious already that Kairi is her official successor.
Sora's boss fight against the Ice Clawbuster in Trickster's Paradise is a pretty cool fight. Right before the fight the boss freezes Monstro, and you actually fight around the frozen whale. Near the end of the fight, the game prompts you to hit a crack on Monstro so you can use your Reality Shift on him. What follows is literally chasing the boss on Monstro which is encased in a bubble.
Likewise, his fight against Rinzler is pretty cool, since it uses the gravity gimmick that was seen in the actual movie, and you can use Reality Shift to disable his discs, leaving him running around waiting for them to reactivate. Though for some players, this may fall into Tear Jerker territory, considering you're fighting Tron, trying to get him back to his senses, and what happens after the fight.
Lets give a nice mention to one of the greatest level designs in the Kingdom hearts series so far: Symphony of Sorcery. The Fantasia level, Square took the source material and RAN WITH IT. The actual levels are silent; no grunts, shouts, or magic spells, and the sounds made by the Dream Eaters are heavily muted. Instead, you listen to the grand, sweeping orchestral composition from the original movie. Songs include: Waltz of the Flowers, The Russian Dance, The Sorcerer's Apprentice, and yes, NIGHT ON BALD MOUNTAIN! No techno, no remixes, just the full pieces as they were meant to be. Walt would be proud.
On the subject of Fantasia: Chernabog. Yes his boss battle was easier than expected, and more or less just a Dive sequence. That doesn't make it less awesome, hearing his music, and seeing him create fire storms and ghosts.
Also on the subject of Symphony of Sorcery world is the chock full of references for fans of the original move. Notable ones being that Sora's Reality shift flowers on the cloud part of his world are Dionysus' goblets overflowing with wine and you can find the benches the Centaurs sat on in the movie as well.
Also mentioned on the Heartwarming page, Riku gets one in one of the last cutscenes. When Ansem the Wise in the dreamscape asks Riku what his name is, he answers, "Riku," before leaving. In Kingdom Hearts II, when Ansem the Wise as DiZ asked Riku during the time he took on Ansem SOD's appearance, he answered "Ansem" instead. It just shows how much Riku's grown as a character and that he is done letting the darkness in his heart control him instead of the other way around.
The battle with Pete and the Beagle Boys is pretty awesome. Much like with Prankster's Paradise, you get to (have to) use Reality Shift for the finishing blow.
Riku vs. Ansem, Seeker of Darkness and the entire cutscene leading up to it. Ansem, as usual, is trying to goad Riku to embrace the darkness, tempting him with the promise of being able to rescue Sora. Riku then calls out Ansem on how he now knows the truth of Ansem being the heartless of a former Keyblade Master, and how Darkness stole away his right to wield a Keyblade; He uses this to show the difference from him and Ansem, even after all this time and all of his struggles, he STILL wants to prove himself worthy to wield the Keyblade rightfully, and then mentions his encounter with Terra (who, initially wanted for Riku to become a worthy Wielder and Master someday when he gave him the Rite of Passage). Riku resolves now to go to the real world to Sora's aid—completely rejecting Ansem's offer and showing that Ansem will not get to him ever again. For once in the series, things are not going according to Xehanort's plan, and he is pissed. Cue an epic, three-phase boss battle, which culminates in Riku echoing the words he told Terra years ago, accompanied by his leitmotif.
The inclusion of Mickey, Donald, Goofy: The Three Musketeers into the series' lore gives the Disney trio a pretty awesome bit of Fridge Character Development. In the film, the reasons why they aren't being made Musketeers is: 1. Donald's a coward, 2. Goofy's an idiot, and 3. Mickey's physical stature prevents him from being useful. The film ends by basically saying that they cover for each other's shortcomings and can become better together. This is exactly what happens in Kingdom Hearts: Donald's gotten over his cowardice, Goofy routinely picks up on things faster than Donald or Sora, and Mickey is one of the most powerful characters still active in the story. Even better, all three of these things were true for the original Kingdom Hearts, which precedes the movie by two years.