Heartwarming / Harry Potter and the Methods of Rationality
Instead of living with nasty relatives, Harry grows up with loving parents, with Petunia being a good mother, albeit one that doesn't take a boy like seriously enough to his liking.
Quirrell's Christmas gift to Harry. Assuming it's not a trap.
When Harry and Quirrell are walking down the street, and Quirrell's very presence causes leaves to wither, notes to sour, and hearts to break. Harry doesn't say anything, because even a grinch needs a merry Christmas.
Hermione thanking Harry for defending her.
What Hermione did in "Humanism".
Harry's happy thought in Humanism.
Harry's (first) Christmas wish.
The bit where Draco calls forth a Patronus in chapter 47 through his love for his father and the memory of him holding his hand and helping him when he thought he was about to die. Say what you will about Lucius and Draco, but that love is genuine and powerful and Draco's reaction to seeing it manifest is beyond sweet.
On that same chapter: "Every life is precious, everything that thinks and knows itself and doesn't want to die. Lily Potter's life was precious, and Narcissa Malfoy's life was precious, even though it's too late for them now, it was sad when they died. But there are other lives that are still alive to be fought for. Your life, and my life, and Hermione Granger's life, all the lives of Earth, and all the lives beyond, to be defended and protected, EXPECTO PATRONUM!"
Harry's scene alone on the top floors of Hogwarts, in the last chapter before the hiatus.
"You can never have enough books. But you certainly tried. It was a really, really, really good try."
Real Life - CMoH: "Mr. Hagrid is innocent. Ridiculously obviously innocent. He is the most blatantly innocent bystander to be convicted by the magical British legal system since Grindelwald's Confunding of Neville Chamberlain was pinned on Amanda Knox." (Read the last phrase of the author's notes.)
Harry gives up all his money and goes deeply into debt to Lucius Malfoy, of all people, to save Hermione.
Quirrel is genuinely thankful when Harry arranges an event to entertain him when he is bored marking essays. Admittedly the event involved traumatising bullies with a dark ritual, but hey.
Harry is truly grateful and hugs Neville when he says he still wants to stay even after Hermione dies horribly.
Doubles as a Tear Jerker, but Hermione's final words at the end of Ch 89. Remember Harry's lecture on accountability in Ch 75?
Harry: "You could call it heroic responsibility, maybe. Not like the usual sort. It means that whatever happens, no matter what, it's always your fault."
Hermione's words to Harry fourteen chapters later? "Not your fault."
Lucius, after seeing Draco's newfound effectiveness from rationality training: "He will be the greatest Lord Malfoy that has yet lived." No hesitation, Lucius is just so proud of his son that he immediately declares Draco will be superior to him and all his vaunted ancestors.
"No matter what is happening, remember that we love you and will always love you no matter what. I don't know if our love has any magical power under your rules, but if it does, don't hesitate to call on it."
The last conversation between McGonagall, Harry, and Snape in Chapter 121 counts for sure, with Harry forgiving Snape for everything he did, Snape and Harry finally having a real talk about Harry's parents, and Snape deciding to leave Hogwarts and try to do good in the world. Also, the advice Harry gives Snape, which also serves as their last words to each other.
Harry: "Ruminating about the past can lead to depression. You have my blanket permission never to think about your past, ever. You shouldn't think it's your responsibility to Lily to bear your guilt for her, or anything like that. Just keep your mind on the future and whatever new people you meet."
Snape: "I shall take your wisdom into consideration."
Harry: "Also, try a different brand of hair shampoo."
Snape: (smiles wryly, as in actually smiles) "Drop dead, Potter."