After Kala takes Tarzan to the remains of his parent's tree house, he exits wearing his father's clothes intending to leave the jungle to be with Jane, but before he leaves, he embraces her one last time and tells her, "No matter where I go, you will always be my mother."
Any scene between Kala and Tarzan. Gorilla mom is best mom.
"You came back?" "I came home."
Kerchak's last words. Two of them in particular - "My son."
After Kala finds baby!Tarzan and brings him back to the group. When they go to their tree to sleep, Kala and then Phil Collins sing "You'll Be in My Heart". The whole scene just makes you wanna go "d'awww".
When Tarzan is boarding the boat to go to England with Jane and her group, she excitedly tells him about all of the fantastic things he'll see and people he'll meet. All Tarzan wants to know is if he and Jane can stay together for it all. Aw!
Jane deciding to stay with Tarzan in the jungle rather than go back to England. Her father deciding to stay as well is just icing.
Jane: Oo-oo-e-ah-oo. [cheers from Tantor and the rest of the gorillas]
After how initially frightened she was of Jane, it was very cute to see Kala taking her by the hand and welcoming her with a smile. Doubly so because it was Jane who first noticed Kala hadn't been freed from her cage and took out the captors who were trying to get her on the boat.
At the beginning when Tarzan's father is struggling with the beam and his wife goes in to help him carry it. The looks of sheer determination on their faces is inspiring.
Tarzan's parents in general. The only survivors of a shipwreck, deserted on an island with no escape, a newborn in tow, it's amazing they lasted as long and as well as they did and that's mainly because of their dedication and teamwork. Despite everything, they did their best to live in the jungle and create a (sadly short-lived) home from them and their baby.
The moment when Tarzan finally finds another (Jane) whose hand matches his.
Meta example: The guy in charge of animating this scene, Glen Keane, said he achieved that look on Tarzan's face by remembering how he himself felt when he held his newborn daughter for the first time. He then tells her, "That's not Tarzan looking at Jane; that's me looking at you." *sniff* J-just give me a minute...
This conversation between Jane and her father.
Archimedes: Jane, dear, I can't help feeling that you should stay. Jane: [tearful] Daddy, please don't. We've been through all of this, I couldn't possibly st-. I-I belong in England, with you, with people! [Jane's glove is blown away towards Tarzan and he picks it up] Archimedes: But you love him.
Tarzan showing Jane how to swing a vine. When Jane first jumps, we see her hugging tightly to the vine in terror but then she opens her eyes and immediately starts enjoying it. The look of happiness on her face can't be described.
And as Tarzan swings with Jane, their vines end up getting wound together - the way he looks at her must be seen to be believed. And Jane grinning and looking away bashfully is adorable.
And before that, she's trying to sketch a bird but it flies off before she can finish. So Tarzan takes her up into the tree top where there are hundreds of birds.
Both funny and heartwarming, but the baboons chasing Jane earlier return during the final battle to save her from Clayton's men. The baby baboon is wearing her boot as a hat and kisses her on the cheek when he sees her again.
The fact that the baboon clan waits until the baby orders them to charge before attacking; they realise that Jane is, despite looking different, one of the jungle folk and no-one fucks with a jungle folk.
Seeing Kerchak, huge and imposing as he ordinarily is, playing with his and Kala's baby at the very beginning of the movie is pretty cute.
The look Kerchak gives Tarzan after he defeats Sabor. He almost looks proud of him.
Any time Terk shows that she really does care about her cousin. For example: when she and Tantor were rescuing everyone on the boat, she hugs Tarzan and sobs "I thought I'd never see you again!"
Listen to the reprise of "You'll Be In My Heart" from the stage musical. You WILL cry.