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Tear Jerker: The Jungle Book
The original books
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
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 blisfully unaware Mowgli, which is rather painful to watch.
Baloo: I love that kid. I love 'em like he was my own cub...
Bagheera: Then do what's best for him.
And during that scene, Mowgli is happily singing "The Bare Necessities" and gets excited for a fun day with his friend, which gives Baloo doubts about breaking the bad news to him.
And a bit later, when Mowgli feels betrayed when Baloo tells him he should go to the man-village, then running away and abandoning him.
Mowgli:(to Kaa) I don't trust anybody anymore.
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.