The Winnie the Pooh series thrives on heartwarming, particularly the Disney installments, so picking out examples is difficult. But here's a shot anyway...
One moment from The House at Pooh Corner deserves special mention: Piglet giving up his own house to Owl. Followed by Pooh immediately telling Piglet that he can come and live with him.
In the last book, The House at Pooh Corner, the final scene (with Christopher Robin and Pooh spending their last childhood day together before Christopher Robin goes off to school) is a several-pages-long Heartwarming Moment, and ends with these words:
So they went off together. But wherever they go, and whatever happens to them on the way, in that enchanted place on the top of the forest, a little boy and his bear will always be playing.
Even Return to the Hundred Acre Wood, for all its flaws, manages to pull off a Heartwarming Moment ending, that's somewhat reminiscent of the original ending but still does its own thing. Christopher Robin, after spending the summer with his friends, has to leave and go back to school again, and Pooh and Piglet philosophize over the changing nature of things before going off together:
So off they went, together. And if you pass by the Hundred Acre Wood on an early autumn evening, you might see them, arm in arm, strolling contentedly under the trees, until they are swallowed up by the mist.
The scene in The House at Pooh Corner where Pooh sings a song to himself while trying to decide who to visit ("I could spend a happy morning seeing Roo/I could spend a happy morning being Pooh"), but then goes tramping off to Piglet's house, while the narration reveals that that's what he'd planned on doing all along:
I could spend a happy morning seeing Piglet,
And I couldn't spend a happy morning not seeing Piglet...
The story where Pooh and Piglet try to give Eeyore a hunny pot and a balloon respectively. Pooh winds up eating the honey and Piglet accidentally pops the ballon. They pass the empty pot and shredded balloon as their gifts, saying that they got him "a useful pot to put things in and something to put in it as well." Eeyore ends the story happily putting the balloon into the pot and taking it back out over and over again.
Every time Christopher Robin chuckles and says "Silly old bear". Cutest Catch Phrase ever.
The entire "Places in the Heart" sequence at the end of Winnie the Pooh: A Valentine for You
The ending of the Pooh segment in Kingdom Hearts II, when Sora indicates Pooh's heart and tells him that he can always find him there.
In Pooh's Super Sleuth Christmas movie, when Pooh and his friends give up trying to save Christmas a lost cause, but Darby convinces them to keep going.
The "Little Mr. Roo" song from Pooh's Heffalump Movie
This scene between Chris and Pooh from the ending of Pooh's Grand Adventure:
Chris: "Pooh, promise you won't forget about me, ever. Not even when I'm a hundred."
Pooh: "How old shall I be then?"
Pooh: "I promise."
The exchange comes from the last original novel, The House At Pooh Corner, as shown above. The Disney version, for some reason, changes these end lines from the book and delivers an ending that, while still a legitimate Heartwarming Moment, is a bit more of a Tear Jerker:
Wherever they go, and whatever happens to them on the way, in their enchanted place on top of the forest, a little bear will always be waiting.
Tigger: Only the best, for my bestest little brother...
Roo's entire view of Tigger throughout the movie counts as heartwarming or a Tear Jerker. While Roo had always been friends with Tigger throughout the Disney features, The Tigger Movie expands as to why; he wants a big brother to look up to (he even has tons of drawings of him with Tigger together hanging on his bedroom wall, he outright idolizes him). It is somewhat fitting that The Tigger Moviebegins Roo's expanded role in the series. This was expanded on a bit more in Springtime With Roo where we see Tigger's perspective of their friendship and his desire to keep Roo happy.
There's something heartwarming about the scene where Pooh tries to sing the bees to sleep, while Piglet and Eeyore wait around for him to come back. If you just came off watching the original Pooh movies, it gives you the feeling of being home again.
The credits of The Tigger Movie, which feature Ernest H. Shepherd-style illustrations of everything that happened in the movie, while Kenny Loggins' "Your Heart Will Lead You Home" plays.
The trailer alone for the 2011 movie is enough to leave you teary-eyed. The use of Keane's song "Somewhere Only We Know" is brilliant in itself. Even the usually snarky and harsh YouTube repliers filled the video's pages with touching comments about how they watched it and felt like a child again!
In the end of the 2011 film, when Pooh chooses to bring Eeyore his tail back instead of receiving honey (after looking for it the entire movie). This proves that the only thing he loves more than honey are his friends. Also this little exchange.
Pooh: "So are you happy, Eeyore?"
Eeyore: "No. (Beat) But I sure do like this new tail. Thank you, Pooh."