This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Jungle Book
The original books
Mowgli leaving the jungle for the very first time. He just witnessed almost the entire wolf pack, who had always been his family, turn against him because of Shere Khan's manipulations, and try to kill both him and Akela. It's even the first time Mowgli actually cries in his entire life.
"What is happening to me? What is wrong with my eyes? Bagheera... am I dying?"
In "Red Dog", Akela's death. After helping the Seonee Pack fight off the dhole, he succumbs to his wounds but not before telling Mowgli his debt to the wolf pack is repaid and he must return to men.
When Mowgli leaves the jungle for the last time to return to the world of men and must say good-bye to his animal friends.
The Disney animated film
When the Wolf Pack came to the decision to cast out Mowgli from the pack because Shere Khan would kill not only him but everyone in the pack, they don't take any joy and are very saddened by the fact that Mowgli would surely die. They really saw Mowgli as nothing more but a child and saw no pleasure in thinking they are sending him to his death.
That moment when there's a very real chance Baloo had been killed by the tiger.
Baloo "coming back to life", while Bagheera is still eulogizing him.
"Greater love hath no one than he who lays down his life for his friend. When great deeds are remembered in this jungle, one name will stand above all others: our friend, Baloo the bear. The memory of Baloo's sacrifice and bravery will forever be engraved on our saddened hearts. This spot where Baloo fell will always be a hallowed place in the jungle, for there lies one of nature’s noblest creatures."
Bagheera finally convincing Baloo to take Mowgli to the man-village. Despite knowing Mowgli for all of a day, a great deal of attachment and devotion has been placed onto Baloo, making his realization that he will have to let him go (and break his promise) genuinely emotional. And his desperately trying to get around to explaining this to the blissfully unaware Mowgli, which is rather painful to watch. Mowgli feels betrayed when Baloo tells him he should go to the man-village, then running away and abandoning him.
"My Own Home" is just a haunting tearjerker of a song.
Mowgli's second encounter with Kaa shows how hurt he is by Baloo's betrayal.
Mowgli:(to Kaa) I don't trust anyone anymore.
Also, Mowgli seems rather... less scared of Kaa than you'd expect, since he clearly knows Kaa wants to eat him. While he's clearly trying to resist Kaa, he doesn't seem especially scared, and doesn't even try calling for help, likely because he knows who would come. It's like he's so depressed by this point that a part of him doesn't really care if Kaa eats him or not, just as long as he doesn't have to leave the jungle.
Kaa: It's like you said man cub, you can't trust anyone!
The final scene where Baloo just stares blankly for a moment when Mowgli shrugs and walks away, and then is coaxed by Bagheera into pretending as if everything is just fine, since Mowgli is safe where he belongs.
The Cut Song "The Mighty Hunters" almost makes Shere Khan appear sympathetic.
After the film was completed, Disney's personal nurse, Hazel George, went up to animator Ollie Johnston in tears, saying that the way Baloo and Bagheera danced off into the sunset together was perfect, since it was the same way Walt had gone out.
The 1994 live-action film
Mowgli crying while holding Baloo, who got shot helping him. He got better at the end.