The Small One: everything from "I need a gentle donkey, to carry my wife to Bethlehem" to the end.
"He's good enough to be in a king's stable!" The love between Small One and his master is palpable.
This troper always remembered the tanner as a terrifying villain, but after rewatching it, the tanner is actually a very decent man. He can tell the little boy is nervous, and while he's sharpening a knife the whole time he seems to make a conscious effort to be as unthreatening as possible. When he realizes that the child doesn't understand who he is, he also explains "Boy... I'm a tanner. I only want him for his hide..." in as gentle a manner as possible when it would have been simple to just say "Sure thing, kid, I'll take real good care of him". Small One likely isn't the only old, loyal friend that he's had brought to him, and while the nature of his work doesn't let him have too much empathy for the donkey, the tanner is nevertheless a good man and the gentleness he showed the two is a welcome contrast to the mocking auctioneer later on.
In Brother Bear, when Koda snuggled up to Kenai, mumbling "I always wanted a brother..."
Koda throwing himself into Kenai's arms, dispite Kenai now being human. AAAW.
Kenai choosing to remain a bear so he can watch over Koda.
Darling is singing to her new baby, and Lady comes into see, then Jim Dear enters and holds Lady up so she can see the new baby and looks at it and wags her little tale, and both Jim Dear and Darling pet her. Lady is so sweet.
The ending, Lady is all grown up, Tramp is adopted and they have a litter of puppies.
From the sequel, Scamp's Adventure, we get the entire sequence of "I Didn't Know I Could Feel This Way"
Gummi Bears in "Up, Up and Away," when Cubbi is so moved by Gruffi's parting gift, a plaque with his likeness entitled "Sir Cubbi" that he tells the departing Chummi that he can't leave his family, regardless of the fact that he is throwing away seemingly his one chance of being a knight. When he returns, the Glen Gummis, Cavin and Princess Calla make it up to him by arranging a formal ceremony where the Princess fulfills Cubbi's dream as best she can by dubbing the young Gummi "The Unseen Knight and the Secret Defender of Dunwyn."
Even Bonkers had one of these. In "Is Toon Fur Really Warm?", the scene where Marilyn and Skunky Skunk hug each other and this is after Skunky said he doesn't want to do a girls' birthday party because it would ruin his reputation and make him look soft. Jerk with a Heart of Gold, anyone?
Marilyn (holding Skunky):You'll always be my favorite even though we'll never meet. Say, you're pretty warm. What am I talking about? It's just a doll.
Skunky (springing to life):Nope-a-roo! It's caaaandid skunk!
Marilyn:Skunky! It's you! (they hug)
Furthermore, The Fluppy Dogs pilot had a gently subtle one. The young boy, having just gotten one of the Fluppy aliens, Tibby, out of the pound is told that he can't keep her, but he should offer her to a teenage next door neighbor, Claire. The boy, convinced that the girl hates him, comes to her front door to first awkwardly apologize for bugging her before trying to convince her, preparing for her to blow up in his face. Instead, he has that great moment a child's life when he realizes when someone he fears turns out to be far more pleasant than expected when she forgives him, just before her heart melts at sight of Tibby.
The finale for Pepper Ann should also count.
The ending of the Mickey Mouse short "Tokyo Go" counts as well.
A meta-example: Has anyone noticed the back-to-back movies in Disney's Sizzlin' Summer block? Entirely Pixar. Either John Lasseter being the CEO has something to do with it, or Disney's finally forgotten their buyout of Pixar for a summer and said, "Hey, guys...we have a surprise for you...instead of wasting our time on our movies...let's let you have a month instead. You earned it." Sure, to some it sounds like a cheap cop-out. But to others, it means—perhaps there is a heart underneath all the merchandise.
Or they finally realized the true profitability potential of showing lots of Pixar movies on TV.
The the ending to the new Mickey Mouse short "Potatoland", where Goofy is touched when Mickey admits that he and Donald made a potato theme park to make Goofy happy.
Goofy: Potatoland may have been a dream, but our friendship is real.
Real Life Events
In the documentary Pursuing Happiness, Richard Sherman recalled that when he was giving a lecture to a college, a student asked him how much money he made from the song "Winnie the Pooh". He responded by recalling an event from the Baby Jessica fiasco from 1987 where she asked her mother from the well to sing the song to her, saying that if Pooh can get out of a tight spot, she can too.
Walt Disney's daughter, Diane Disney Miller, spent her last years reminding the public about the humanity obscured by her father's corporate image. One way she did this involved opening the Walt Disney Family Museum. She also recorded intros for the Diamond Blu-Ray Discs of her father's animated movies, placing each in the proper context of his career. She didn't live long enough to record intros for all of these releases, and by an unbelievable coincidence, the last release confirmed to have her is The Jungle Book-the last animated movie made under Walt's supervision.