At the end of the game, Riku admits that he's always been jealous of Sora, and then...
Riku: But there is one advantage to being me. Something you could never imitate. Sora: What's that? Riku: Having you as a friend. Sora: Then I've got something you could never imitate too.
The ending of the game. Also, when Sora gets tackled in a hug by Donald and Goofy and Riku catches Mickey and spins him around.
Sora: We're... we're back. Kairi: You're home.
Hell, almost every scene in the ending; Mickey and Minnie reunited, Beast (now human) dancing with Belle, Jack with his ship, Nala and Simba having a child, Ariel married, Leon reading a letter from an old friend, Sora at Destiny Islands finishing off Kairi's drawing.
Sora was not actually finishing Kairi's drawing. She already did at the end of the first Kingdom Hearts game. Sora merely touched the drawing of Kairi's Paopu Fruit, realizing that Kairi loves him too. Even more heartwarming is that Kairi's Paopu Fruit is so much bigger than Sora's Paopu Fruit towards Kairi. A symbolic reason being that Kairi really loves Sora so much, possibly much more than Sora does towards Kairi as to him, it was just wishful thinking until Kairi reciprocated his feelings although the two have not admitted to each other their feelings in person.
The entirety of the reunion between Mickey and Minnie. Dear lord, if anyone deserves a happy, heartfelt reunion that is not interrupted by Heartless, nobody or some other adversary trying to kill them, it is those two... and they get one!
Then, there's the music. It's an upbeat version of Disney Castle's theme that hits the crescendo as we see King and Queen reunited. Then, as they touch, hands to hands, nose to nose, the music settles down into their romantic theme.
Mickey boops his wife's nose with his own. And Daisy crushes Donald in a glomp.
All throughout Kingdom Hearts I and II, Minnie never loses faith that her husband will come back to her. And, at the end, she's proven right. He comes home to her.
"Sora will find the answer we're looking for. I know he will. Because he's me." Though it at first sounds odd, and maybe even egotistical, I can't help but smile every time I think of this moment from KHII: Final Mix. Through most of the game (especially with scene additions), Roxas makes it clear that he wants his own identity, that he doesn't want to just be Sora's Nobody. He lashes out at anyone who calls him Sora, and continuously says his heart belongs to him. But now he's accepted the fact that Sora is a part of who he is, but not all he has to be, and that they can learn to coexist without having to give up anything.
Pluto trying to comfort Kairi in the prison cell of the Castle That Never Was. Heck, Kairi and Pluto's unexpected yet incredibly sweet friendship in general qualifies here.
Mickey and Donald's reunion with Goofy after his Disney Death.
Before that - Donald and Mickey care for Goofy so much that the thought of him being dead is enough to make Mickey officially become dangerous (and, to note, Mickey is 2'7" tall. That's about the height of a five year old, maybe a six year old) and to make Donald's furious anger become useful in making him so infuriated with rage that he goes after the Heartless with a vengeance.
Hell, even before that. Goofy is willing to die for Mickey. A true friend, even to the end.
Sora and Kairi hugging, especially Kairi's line when she actually feels Sora: "This is real."
Tron's goodbye after defeating the MCP.
It's even more Heartwarming in Hindsight. Kingdom Hearts 3D: Dream Drop Distance reveals that programs are somewhat like Nobodies, as they don't have hearts either. The same game confirms that Nobodies can grow their own hearts, given time, and it's quite possible that the same could go with programs. Tron is a program, and thus does not have a heart at first: his friendship with Sora allowed Tron to grow one of his own!
Tron leaves a little 'thank you' message that shows sprite images of Sora, Donald and Goofy jumping up and down in the most adorable way.
A little tiny one: After Mickey reaches the unconscious DiZ (who, of course, is actually Ansem the Wise) in The World That Never Was, the latter starts to stand up. DiZ stumbles for a moment, then glances at Mickey, who he's using to support himself. He pauses for a moment before standing, which this troper interpreted as giving his old friend a hug.
One before that: Mickey reaches the place where DiZ is... and takes less than half a second to take in what is going on, that his friend is being attacked, before unleashing all of the shit on the Nobodies to save his friend. Talk about friendship.
DiZ is about to die by exploding. Mickey races towards him to try and save him and Riku has told hold Mickey back; Mickey is willing to die in an explosion to save his friend.
A rather nice little moment occurs while Santa and Sally are talking. While chatting Maleficent and Oogie Boogie attack them in an attempt to capture Santa. Despite not knowing Sally for more than a few minutes, Santa valiantly puts himself in front of her and their attackers. Pure of heart? That's Santa Claus alright.
The little pep talk Santa gives Jack is rather sweet as well, pointing out that despite their different methods they still bring joy to people's hearts, and Jack should take pride in his work.
Just the cutscene before entering Christmas Town can warm a heart. Sora and Kairi stopped believing in Santa Claus when they were eight years old because Riku told them that he didn't exist. Then Sora gets the chance to meet Santa himself. Seeing the door to Christmas Town, he becomes more and more exited, until he loses his patience and asks Jack to "just open it". The main heartwarming part is that, up until this point, he's been a Stepford Smiler who's hardly had any chance to be purely happy (especially given Port Royal had a Yank the Dog's Chain/Team Rocket Wins moment against him). This is a rare moment where his smile is genuine.
If (by some incredible chance) you lose to Setzer in the Roxas prologue, Roxas returns to his friends looking disappointed. The four are silent for a moment. Then Pence starts clapping, followed by Hayner and Olette.
When Donald and Goofy finally get to reunite with Mickey at Hollow Bastion. They'd seen him before at Twilight Town, but this time they actually get to run up and hug him.
Yuffie and Aerith fighting together (albeit somewhat offscreen) during the attack on Radiant Gardens and within the 1,000 Heartless War; when Yuffie collapses from exhaustion, Aerith busts out a Curaga spell to keep her ally going.
When Sora reassured Riku with a silly face to help cheer him up when he started Angsting. Riku actually starts laughing.
Quite a few of Sora's Limit Breaks that he has with his party members. Sora high-fives both Aladdin and Tron when performing one with them, Beast rests his hand on Sora's shoulder before unleashing a final attack, Sora and Jack Skellington dance together, and Sora and Riku share a fist bump after wrecking carnage.
Beast has to choose between his rose or Belle - becoming human, or staying as a Beast - and goes for Belle. Being human is not worth losing her.
To add to this: Belle willingly chooses to stay with Beast when she's offered the choice - she could go and leave him and go home, but she chooses to stay with the man/Beast she loves. If the first game wasn't enough to confirm their love... this game is.
Even more heartwarming is that, no matter how much Xaldin got under his skin, Beast never hurt Belle or the servants. He locked his servants away to protect them and Belle remained entirely unharmed by him. He didn't have to be nice to her, as Belle herself said, but he chose to be, even if he was sinking into his hatred and anger and rage.
The fact that Belle cares enough for Beast to make the choice herself - she elbows Xaldin in the stomach, snatches the Rose and runs, just so Beast doesn't have to make the Sadistic Choice.
We get the scene of Sora allowing Demyx to use his Olympus Stone, despite the objections of his friends.
Also Kairi allowing Demyx to return her to her cell after she escapes because he's practically in tears over what Saix will do to him if he fails. Kairi later tells Riku that she empathized with Demyx and Axel.
When Sora manages to snap Donald and Goofy out of a Heroic B.S.O.D. when the trio find themselves trapped inside a computer after being sentenced to death by the Master Control Program and their only means of escape is accidentally destroyed.
Sora: Don't give up! Don't you remember? When we get out of here, we get to see the King. What's the big deal about parts, anyway? If we can't find one... we can make one!!!!
Upon returning from Timeless River, we see that King Mickey has secretly shown up, ready to help out with saving Disney Castle... only to learn that they already succeeded.
Upon playing the game, it adds a second later of heartwarming. In the game, Minnie says "Oh, King Mickey, I wish you were here..." before calling for Donald and Goofy. Well, Minnie, your husband heard you and came a-runnin'.
Upon defeat, Xigbar seems to be rooting for Sora. Nice to know that even if he is half-Xehanort, he is able to fight back somewhat.
Kairi is nothing but a stranger to Olette, but she immediately offers Kairi a place to stay while she waits for Sora to return to Twilight Town.
When Axel shows up to kidnap Kairi again, Heyner and Pence move to stop him, just like in the game, but are stopped when Axel sets their hair on fire. And Olette? Olette grabs a bat and tries to help protect Kairi without a second thought.
When Sora seems down about finding Riku again, Aladdin takes his hands in his and tells him not to give up. Sora's companions in general are more affectionate towards him in the manga.
Tron's smile after Sora declares that they're friends is so heartwarming, especially since Tron has only just started to come out of his shell around them.
Axel actually goes back to rescue Kairi from the dungeon and apologizes for kidnapping her, even though she's none too pleased to see him again. When Saix attacks and Axel fends him off, Axel even looks genuinely relieved that Kairi wasn't hurt by the altercation.
Kairi's reunion with Riku is shown more in full. After she pulls back his hood to reveal Ansem's face, he averts his eyes and tells her he didn't want her to see him looking like that, but she just pulls him into a hug immediately.
In Chapter 63, when Riku in the form of Xehanort's Heartless revealed to Sora that Roxas is his Nobody, Sora symbolically joins Roxas in the symbolic Twilight Town above the clock tower to show that he is not alone. One of the panels shown is exactly the same as the title screen of Kingdom Hearts II Final Mix's after completing the game for the first time.