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.
Ron, Fred and George showing up to rescuse Harry from Privet Drive and bring him, home. If that's not real friendship then I don't know what is.
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.
Not to mention, she mentions that she and Arthur were seriously considering going to get Harry themselves.
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. Especially since it actually cheers Harry up a little bit.
A very brief moment, but Percy gives some simple advice to Harry when the latter is choosing his course list for third year; no condescension and almost no bluster. Granted, Harry doesn't consider it helpful, but points for trying.
At the end of the novel, Ginny of course blames herself, despite the fact that this is in no way her fault. And Dumbledore tells her as much, getting her some hot chocolate and assuring her that she's not the first (or, sadly, the last) to be conned by Lord Voldemort, and that no punishment will come to her.
When Harry gets called to talk to Dumbledore after the attack on Justin and Nick, he worries he's going to be accused. Apparently Hagrid had the same worry, because he immediately bursts in swearing up and down that he was with Harry only minutes before the attack, and he'd swear in front of the Ministry itself if he had to. Granted, that's not at all what Dumbledore wanted, but it's still sweet.
From the Film
At the final feast of The Chamber of Secrets, Hermione races the length of the hall to hug Harry and has an awkward reunion with Ron. Then, Dumbledore makes his speech — but, what's this? A door opening! Who dares to interrupt the great and Powerful Dumble— Oh, It's Hagrid! Carry on! Cue the biggest load of tears (up to this point!) that anyone will ever give as, the first thing Hagrid 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: "It's not Hogwarts without you, Hagrid."
Doubly touching when you remember that to Harry, Hogwarts is the first true home he's ever had. And without Hagrid, it couldn't possibly be the same...
Completed with a big hug afterward. Professor Dumbledore is the first to applaud, but Professor McGonagalll is only two seconds behind Dumbledore to clap Hagrid's return; Madam Pomfrey is beaming with joy; Professor Sprout — the take-no-shit-when-her-school-is-in-danger teacher of Deathly Hallows — is crying with Joy! Cue the massive standing ovation from the entirety of Hogwarts!note Except Draco and his gang of friends, naturally. But the rest of Slytherin House was standing and cheering; hell, Snape was on his feet!
Possible YMMV, but there is one scene that the movie does better than the book: In the book, Harry kills the Basilisk, is poisoned, and is then saved by Fawkes. Voldemort comments on Phoenix's healing powers before Harry destroys the diary. In the movie, Harry destroys Voldemort before Fawkes heals him; Ginny wakes up to see him still wounded. He ignores the fact that he's dying, and tries only to calm her down and get her out of the chamber safely. Because that is the kind of person Harry is.
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.
It's not small at all. It's a microcosm of the point of the entire series. Where we came from doesn't matter. Our choices do.
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!