Heartwarming: Harry Potter and the Philosopher's Stone
From the Book:
Dumbledore explaining why Harry survived Voldemort's attempt to kill him:
"Your mother died to save you. If there is one thing Voldemort cannot understand, it is love. He didn't realize that love as powerful as your mother's for you leaves its own mark. Not a scar, no visible sign... to have been loved so deeply, even though the person who loved us is gone, will give us some protection for ever. It is in your very skin. Quirrell, full of hatred, greed, and ambition, sharing his soul with Voldemort, could not touch you for this reason. It was agony to touch a person marked by something so good." Dumbledore now became very interested in a bird out on the window-sill, which gave Harry time to dry his eyes on the sheet.
Also from the chapter, Hagrid's gift to Harry:
It was full of wizard photographs. Smiling and waving at him from every page were his mother and father. "Sent owls off ter all yer parents' old school friends, askin' fer photos... Knew yeh didn' have any... D'yeh like it?" Harry couldn't speak, but Hagrid understood.
After Harry rants about what will happen if Voldemort comes back and says he's going to go after the Stone, Ron and Hermione decide to go with him without a moment's hesitation, and without even telling him first:
Harry: I’ll use the invisibility cloak, It’s just lucky I got it back. Ron: But will it cover all three of us? Harry: All—all three of us? Ron: Oh, come off it, you don’t think we’d let you go alone? Hermione: Of course not. How do you think you’d get to the Stone without us? I’d better go and look through my books, there might be something useful…
This becomes something of a Brick Joke when Dumbledore describes how the true magic of the Cloak is its ability to cover multiple people all the way in Deathly Hallows.
And later in the same chapter, Ron sacrifices himself in a game of chess so that Harry can go on to stop Voldemort. Keep in mind that these are eleven-year-olds.
In The Philosopher's Stone, when Neville comes back to the common room with a Leg-Locker Curse, Harry gives Neville a Chocolate Frog and tells him, "you're worth twelve of Malfoy." This is made more heartwarming as it was the last from a box he'd got for Christmas (he'd never had Christmas presents before), and shortly after, Neville stood up to Malfoy.
The beginning of Harry and Ron's friendship with Hermione, when they go back to save her and she winds up lying to protect them. It's really all summed up with the classic line, "There are some things you can't share without ending up liking each other, and knocking out a twelve-foot mountain troll is one of them."
From the Film:
The book and film of Philosopher's Stone both have this scene, but the acting by both the late great Richard Harris and young Matthew Lewis puts the filmed version ahead in my opinion.
"There are all kinds of courage," said Dumbledore, smiling. "It takes a great deal of bravery to stand up to our enemies... but a great deal more to stand up to our friends. I therefore award ten points... to Mr. Neville Longbottom!"
This example from Philosopher's Stone?
Hermione: Harry — you're a great wizard, you know. Harry:(very embarrassed) I'm not as good as you. Hermione: Me! Books! And cleverness! There are more important things — friendship and bravery and — oh Harry — be careful!"
Harry's reaction to receiving presents on Christmas at Hogwarts. Considering how the Dursleys most likely never gave him a decent gift all those years, this was definitely a big deal.