Heartwarming: Harry Potter and the Chamber of Secrets
From the Book:
There is also the ending of Harry Potter and the Chamber of Secrets, when Dumbledore finally learns that Harry has been Wangsting that he was only fit to be in the house of Slytherin, the so-called "house of villains." That moment, when Dumbledore proves to Harry that he is better than he gives himself credit for, is a truly magical one.
When Ron, Fred and George bring Harry to the Burrow for the first time, while Molly is furious with her boys for sneaking out and taking the car to get him, she immediately welcomes Harry into her home and takes care of him.
This was a small one, but when Harry and Ron are about to sneak away from class they run into McGonagall. Harry tells her they were going to see Hermione, who is still petrified, and McGonagall lets them go. McGonagall, one of the sternest, strictest, no-nonsense teachers at Hogwarts, tears up and lets them go see their friend. And in the end it is this what helps them solve the enigma.
Harry telling the man who murdered his parents and is about to murder him and his best friend's sister that Dumbledore is a better wizard than Voldemort.
While it's mostly funny, Fred and George doing their "Heir of Slytherin" routine when people think Harry's the Heir of Slytherin.
From the Film
At the final feast of The Chamber of Secrets, Hagrid returns from Azkaban, and the first thing he does is walk up to where Harry and Ron sit, thanking them for helping prove his innocence. Harry then stands up and looks at Hagrid with a smile.
Harry: "There's no Hogwarts without you, Hagrid."
Completed with a big hug afterward. Followed by the standing ovation from almost the whole school. Preceded by Hermione coming back, hugging Harry, and then having an awkward handshake with Ron.
In The Chamber of Secrets, Dumbledore told Harry, who had been doubting that he truly belonged in Gryffindor, to look at the sword he had taken from the Sorting Hat. Engraved upon it was the name Godric Gryffindor.
Dumbledore: "Only a true Gryffindor could have pulled that out of the hat, Harry."
And, when Harry admits he worried that the Hat should have put him in Slytherin:
"It is not our abilities that define us, Harry. It is our choices."
It's a small one, but the scene where Hagrid comforts Hermione after Draco Malfoy calls her a mudblood in Chamber of Secrets gets me every time. note Note that this is a big improvement over the same scene in the book, where Hermione had never heard the term "mudblood" before that day.
Hagrid: Don't you think about it. Don't you think about it for a minute.
Made extra heartwarming, when we later find out he suffers from prejudice on both sides, for being half giant.
Dumbledore's reaction to Fawkes being reborn is adorable. It's basically how everyone reacts to a puppy. The cooing sounds Fawkes made just made things more heartwarming.
Minor Pet the Dog moment, but Lockhart wishing Harry luck during the dueling club was the most genuine thing he ever did.
Harry tricking Lucius Malfoy into freeing Dobby, and Dobby's reaction to his freedom:
Dobby: Master has given Dobby a sock... Master has presented Dobby with clothes! Dobby is free!