Near the beginning of the game, we see Donald walk past some of the Enchanted Brooms from Fantasia. This means Mickey finally made the spell work properly.
Watching Sora willingly jump off the plank of Captain Hook's ship because he believed he'd be able to fly was heartwarming enough. Moments later we get to see his faith rewarded as he soars away before the crocodile can eat him.
Watching Sora and Donald happily reunite thanks to Tarzan, sure it's quickly spoiled by a CMOF, but it's a sign of things to come.
"This boat runs on happy faces."
Of all the places and all the people in all her world the place Kairi felt safest to hide her heart was right next to Sora's, under his protection.
Sora is too afraid to tell Kairi how he feels. How does he show he cares for her? By going to the murals they made for each other as children and scratching in a Paopu fruit. At the end of the game, Kairi does the same thing. 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.
Jasmine has been captured, and Aladdin only has one wish. Genie tells him that he can just use that wish to get Jasmine back, safe and sound. He chooses to free Genie instead, honoring the deal they'd made earlier in the level. Genie then decides to go along with Sora, Donald and Goofy to save Jasmine as "a favor".
It actually one-ups the movie, as the stakes are so much higher than they were in the movie and he still chooses to free the Genie. He trusts that his new friends will save her, and he trusts Genie.
The conclusion to Sora's last visit to the Hundred Acre Wood has him, Pooh, and all their friends looking up at the big, beautiful moon together on a hill, before Sora waves goodbye, and the cover of the book changes to a drawing of Sora holding Pooh's hand as they walk side-by-side.
"Sora, don't forget. We shall always be here. If you'd like to visit again, that is."
When Riku!Ansem is advancing to attack Sora, Donald jumps forward to attack - sure, he's knocked away, but the effort was there.
Kairi bringing Sora back from the darkness and transforming him from a heartless back into his normal state by hugging him.
Sora: Kairi... thank you. Kairi: Sora!
Not to mention Donald and Goofy's happy reaction upon seeing Sora turned back to normal.
Riku's HeelFace Turn when he uses all of his remaining willpower to stop Ansem, now in control of his body, from attacking Kairi, Donald, and Goofy in Hollow Bastion. It's shown to be the last act of his heart that causes Ansem to expel it to the Realm of Darkness. No matter how horribly misguided he became, it's clear Riku started down the path of darkness due to his desire to protect the things that matter.
The cutscene of Sora summoning Bambi, complete with the teen giving the fawn a pat in the head. Twice as adorable in Halloween Town, because of Sora's vampire garb, whichshowsa lot.
Bambi as a summon has some extra significance in context with his movie. Man was responsible not just for the destruction of much of his old home via the forest fire but also caused the death of his beloved mother. The simple fact Bambi is so trusting of Sora, that hes willing to help him out to save the universe is incredibly sweet since he can essentially trust this young man to get his home and family/friends back.
Beast loves Belle enough that he ripped apart the fabric of the universe to get from his castle to her. And, to add to it, his castle is being engulfed by Darkness at that point - Beast's love for Belle is that strong that all of that light from his love for her is enough to save him from Darkness and the ocean between, which both Mickey and Aqua were unable to do.
Goofy defects from Riku's side. The first thing he does after saving Sora's life? Ask Donald to apologise to Mickey for the fact that he is disobeying his orders.
Donald declares they can do it together and defects himself.
Sure, looking back, we know that Mickey would definitely agree with them, but they don't know that: Mickey is their friend, but also their King - he could chop off their heads if they defy him. And they still do it.
When Mickey goes out in the Realm of Darkness, when he locks himself away, with no way out, what is the last thing he does? Thank his friends.
To make it even worse in terms of Heartwarming? Beforehand he's all bathed in gold light and showing off to impress. Then the light fades and he thanks his friends - that time there's no showing off, no impressing, just a friend thanking his friends in what could be the last time they ever see each other.
Belle is freed with the other Princesses. Does she go with them and stand around before you fight Riku? No. She goes back to her beloved books - where else is she going to find information? With her books is exactly where Beast finds her. And then, to top it all off, they dance.
One that we don't learn until Re:Coded but applies to this game. Pluto follows Mickey through a Corridor of Darkness from Traverse Town. Yes, Pluto can tell Mickey's whistle apart from anyone else's whistle and knows that following it will make sure that he is safe. No wonder Mickey trusted him with the super important letter of super important importantness at the beginning and end of the game. He's a good loyal dog.
He then trusts Pluto with a second letter of super importantness which Pluto is carrying at the end of the game.
Ariel's friendship with Sora is pretty heartwarming. They hit it off straight away and become fast friends - notably if you keep Ariel as a party member, she frequently heals everyone in battle. They're Like Brother and Sister for the most part, and Ariel is the only one of the Disney characters to worry about never seeing Sora again.
Mickey leaves without saying goodbye, but leaves Pluto behind to protect Minnie. Pluto is a good dog, and Mickey knows it and Minnie probably does too, so he leaves Pluto behind to keep his wife safe.
Minnie never loses faith that her husband will come home to her. Even though he's vanished without a trace to search for the Heartless, she knows he'll come back to her.
Mickey leaves Donald and Goofy in charge of the mission as he's off searching for answers and the Dark Realms keyblade. Guess what? Goofy may not be the smartest tool in the shed and Donald may have a hair trigger temper, but they are the most loyal people to the King, except for his wife who he cannot ask to put herself in danger, so he asks his friends and they succeed and prove why Mickey was right to put them in charge. Together they can do anything.
While looking for Riku and Kairi, Tarzan repeatedly answers Sora's questions about them with "*&&X%". Jane later translates this as "heart". Sora interprets this answer as "your friends are always in your heart" and is disappointed. But towards the end of the game, it's revealed that Kairi's heart has ALWAYS been inside Sora. Tarzan was always aware of this and tried to tell Sora in the best way he could!
Sora has so little darkness in him that, when he does transform into one, all he can become is a teeny-weeny shadow.
After defeating Ansem, Sora, Donald and Goofy come across Pluto, who has a message from Mickey. The three chase after him, happy and laughing. They have a job to do - and they're going to do it as friends this time.
The cutscene you see when you enter the dalmations room after you find all of the puppy chests. Pongo and Perdita have all of their children back thanks to you. From then on, theyre both sitting up properly, in sharp contrast to when its just the two of them, where they seem almost despondent.