Kala losing her baby and subsequently finding the infant Tarzan, set to Phil Collins' "Two Worlds", a song which itself has made people cry when hearing it.
The Musical adds in a reprise of "You'll Be in My Heart" (sung as a duet between Kala and Tarzan) after Tarzan decides to leave the jungle and return to society to be with Jane. While the musical was seen as So Okay, It's Average, every critic admitted that that scene would reduce the entire house to tears every time.
Tarzan's parents and what happened to them. Picture it: Victorian-age Englishfolk, lost in the rainforest with their infant son after having miraculously survived a shipwreck. Yet they're determined not to just lie there and die. They built a treehouse, working together (when the beam slips on the father's shoulders and the mother joins him to help carry it, that's when the tears start). It's a pretty impressive-looking treehouse, and it seems as though the three of them will at least be able to live comfortably... and then Sabor shows up.
The death of Kerchak, right after he finally accepts Tarzan as his son.
Tarzan (to Kala): No matter where I go, you will always be my mother.
Kala: And you will always be in my heart.
The fact that Tarzan is dressed in his father's clothes during that scene doubles the emotional impact. Something about a well-dressed gentleman hugging a gorilla and reassuring her that she is his mother just increases the poignancy.
Phil Collins' "You'll Be In My Heart" instrumentally played in the score during this scene reeeeaaaally gets the eyes to leak.
Kerchak scolding Tarzan for causing the elephant stampede.
When Jane and Tarzan say goodbye at the end of the film. Yes, it only lasts for a couple of minutes, but the heartwrenching tension is PAINFUL. And then Disney thinks, "Oh wait, this scene isn't emotional enough," so what do they do? Make Jane lose her glove in the wind and conveniently fly over to Tarzan, who picks it up and gives Jane one of the most pitiful looks in the history of Disney animated canon. Oh GOD.
"You came back..."
"I came home."
The moment when Tantor and Terk think they've missed saying goodbye to Tarzan. Terk flies into a sorrowful rage while Tantor simply says, "I'm gonna miss him too."
Tarzan has spent his entire life not knowing why he's so different from his mom, his dad, and his friends. He has no idea who or what he is, and then all of a sudden three humans show up...and he finds out Kala and several other gorillas had known about humans all along. The anger in Tarzan's voice when he confronts Kala about the humans is just heartwrenching.
Tarzan: Why didn't you tell me there were creatures who looked like me?!