Neville's friends walking in on him and his grandmother Augusta at the hospital. Harry (who already knows what happened to his parents, but hasn't told Neville) tries to discreetly get everyone else away before they and Neville see each other, but it's too late.
Neville is unable to look his friends in the eye as a sympathetic Harry is helpless to stop it, all the while Augusta is being very harsh, telling his friends that "he hasn't got his father's talents". She then scolds Neville for not telling them about the fate of his parents ("tortured into insanity", as she puts it), saying he should be proud and not mistaking the pain and trauma for shame.
Neville's poor mother not recognizing him. She always gives him a gum wrapper whenever he visits, and Neville keeps them instead of throwing them away. When she hands him the wrapper, Neville finally stares at his friends expecting them to laugh, but they all look on in horror.
Harry did not think he'd found anything less funny in his life.
Everyone except Harry (who already knows) then starts crying after Neville leaves.
It's made even sadder when you realise that Neville's grandmother is wrong: Neville is proud of his parents - massively so - but he doesn't want people's pity. Harry notes that he's looking around, daring anyone to say anything.
A subtle one with Lupin when Sirius dies: He's just lost the last of his best friends, but instead of breaking down, he's trying to comfort Harry.
The scene where Dumbledore explains to Harry why he wasn't made a Prefect and starts shedding a few tears himself:
Dumbledore: I must confess... that I rather thought... you had enough responsibility to be going on with.
The fact this appears in the chapter header art only makes it hit home more.
Molly's personal boggart of seeing her husband and sons (and Harry) killed. It doubles as a dark Heartwarming Moment of sorts, as it's clear she thinks of Harry as her son, too. Afterwards, when Harry goes upstairs and can't believe that, less than an hour ago, he was worrying about who had become Prefect. That he had "never felt more grown-up in his life", it's like it's just dawning on him how real the situation is and that people he cares about could die. Also, with some Fridge Brilliance: Throughout the books (and especially in Deathly Hallows), we see that Ron feels inadequate and unloved compared to his siblings and friends. But his is the first body that we see Molly's boggart turn into. Also, not even in her absolute worst nightmare could Mrs. Weasley imagine Fred and George being apart, even in death. J. K. Rowling, why couldn't you as well?
Bellatrix taunting Neville about his parents ("Longbottom? Why, I've had the pleasure of meeting your parents, boy!"). It's made all the worse by the fact that we've seen them now. The Tear Jerker is his furious and heartbroken "I KNOW YOU HAVE!"
The scene in Dumbledore's office at the end is this when Harry learns about the prophecy after Sirius' death.
Harry: I DON'T CARE! I'VE HAD ENOUGH, I'VE SEEN ENOUGH, I WANT OUT, I WANT IT TO END, I DON'T CARE ANYMORE— Dumbledore: You do care. You care so much you feel as though you will bleed to death with the pain of it.
Deathly Hallows reveals it to be a Tear Jerker for another reason, but here, Harry's Broken Pedestal moment with his father as a teenager is really sad. Throughout the book, he's full of emotional confusion and psychological trauma, and feels that Adults Are Useless. And to see that his ideal image of his father is not true wounds him in a real way. Especially when he wonders if he really wanted to be like his father anymore after being told by everyone who knew James. He eventually accepts it, much like people in life come to terms with flaws in their heroes or people who they look up to, but it's only salt in the wounds he already had.
The "flaw" in Dumbledore's plan.
"I cared about you too much. I cared more for your happiness than your knowing the truth, more for your peace of mind than my plan, more for your life than the lives that might be lost if the plan failed. In other words, I acted exactly as Voldemort expects we fools who love to act. Is there a defence? I defy anyone who has watched you as I have — and I have watched you more closely than you can have imagined — not to want to save you more pain than you had already suffered. What did I care if numbers of nameless and faceless people and creatures were slaughtered in the vague future, if in the here and now you were alive, well and happy? I never imagined I would have such a person on my hands."
This is basically Dumbledore admitting that, not only did he begin to love his most effective intended weapon against Voldemort the moment he saw how brave and selfless and good Harry had become, he was probably trying to stop himself from caring about anyone this much after what happened to his sister.
After Harry learns about the prophecy, he goes alone to think and just wants to be left alone.
When Harry encounters Luna putting up signs asking for her stuff back, she acts so heart-breakingly nonchalant about the fact that people treat her this way because she's different, and Harry finally begins to understand her in a way he never has before.
The scene where Moody shows Harry a photo of the original Order of the Phoenix. Not only did many of them end up suffering cruel and horrible fates during the First Wizarding War, but they are all smiling and waving at the viewer despite knowing they probably aren't going to make it.
The fact that There Are No Therapists is something of a Tear Jerker, but it hits really hard here. Harry (as-of-yet-unrevealed Horcrux problem notwithstanding) is not only dealing with usual adolescent hormones, which is scary enough, but bore witness to a terrifying series of events at the end of Goblet of Fire and was on the train to his so-called "home" before he even had a chance to process everything. And to make it even worse, the Ministry of Magic, the Daily Prophet, and Dolores Umbridge are putting him through insane amounts of crap and persecution, just because he has the temerity to actually tell the truth about Voldemort. No wonder he completely breaks at the end of the book and actually implies a desire to die at least twice.
Harry's reaction to Percy's letter advising Ron to stop being friends with him. It's particularly sad considering Harry thought he knew Percy well enough that he'd never do something like this. It also makes him understand how bad the rumors are about him, making him understand how Sirius must feel about being called a murderer.
He had known Percy for four years, stayed in his house during the summers, shared a tent with him during the Quidditch World Cup, even been awarded full marks by him in the second task of the Triwizard Tournament last year, yet now, Percy thought him unstable and possibly violent.
Harry's outburst at Ron and Hermoine when they suggest that he teach them Defense Against the Dark Arts. It starts with him thinking it's a joke, but he gets increasingly angry as they smirk at him when he honestly admits that a large measure of luck and help were necessary for him to prevail. It finally culminates in Harry flat-out shouting at both his friends that they have no idea what it's like to be in his position, to have to face the horrors he's faced alone in most cases, moments away from being murdered, tortured or witnessing someone's death; and often suffering moderate (and, in one case, nearly fatal) injuries and barely escaping with his life, and in the middle of it all, he mentions Cedric Diggory (Voldemort's last victim) and how it could just as easily have been Harry instead. It speaks volumes to the regret, sorrow, and hardship he's undergoing and his overall reluctance to meet such unfair challenges.
Harry's Hair-Trigger Temper in general. Hermione and Ron quickly learn to walk on eggshells around Harry, since they're never quite sure if anything they might say will send him flying into another rage. And despite this, they still need to tell him some hard truths and start prefacing their sentences with variations on "Now, please don't start yelling at us again, but." Lesser friends would have fled from someone so unpredictable.
A Harsher in Hindsight moment, when re-reading the book and Sirius scolds the twins and says "This is why you are not in the Order! You don't understand! There are things worth dying for!", a slap in the face considering he dies later on, trying to help his godson.
One must wonder how much this line stuck with the twins, as they eventually do join the Order and Fred indeed does die in the final battle.
Fred's retort is almost worse - "Easy for you to say, stuck here! I don't see you risking your neck!" By the end of the series, both Sirius and Fred would wind up "risking their neck" as a part of the Order, and dying as a result.
The uneasiness and paranoia that Harry develops for a bit in the book, worried that he was an easy person for Voldemort to possess and could end up hurting his friends at any moment. So paranoid and scared is he that he doesn't think of the obvious until Ginny points it out when his friends talk to him: That he had Ginny in the vicinity all along, someone who he knows had first-hand experience with being possessed by Voldemort, and could have asked about her experience to see if it really fits his. Granted he most probably didn't want to open wounds but given how relieved he is when they do talk (he feels like singing Christmas songs with the elated Sirius) much of his fear and doubt could have been avoided by an earlier heart-to-heart.
A small one, but Hermione mentions writing to her parents when she's made a Prefect because "it's something they can understand." She probably doesn't have much contact with them because they can understand so little about her life.
At this point in the series, who's to say she even wants to tell them anything? No doubt her parents have asked her how things were and she can't explain, among other things, that there's an uber-powerful Dark Wizard on the loose that wants her best friend dead.
Following Sirius' death, Harry briefly considers that he may have come back as a ghost and seeks out Nearly-Headless Nick to try and find out. Nick says he's been expecting Harry to approach him, as students who have experienced the death of a loved one often come to talk to him about it. Unfortunately, Nick is only a ghost and ultimately knows nothing more about death than he did when he was alive, knowing only that Sirius did not choose to become a ghost and instead passed on. While Harry's brief hope that he might see a form of Sirius again being quickly crushed is sad, the real sorrow comes from the great melancholy in Nick's lamentation of the feeble imitation of life he chose because he was afraid of death, and how he sometimes wishes he had chosen to move on. It's a poignant insight into a normally comedic side character, and the lonely nature of the ghosts in general.
Harry essentially having suicidal thoughts, when he wants Dumbledore to kill him so the pain of being possessed by Voldemort will stop and he can be reunited with his godfather.
At the age of nine, Luna watched her mother be killed by a spell of her own making.note "Yes," said Luna simply, "my mother. She was a quite extraordinary witch, you know, but she did like to experiment and one of her spells went rather badly wrong one day. [...] Yes, it was rather horrible," said Luna conversationally.; she's said to be "conversational" about it. So either she's accepted it so easily that she can talk about it... or her weirdness is her coping method.
Sirius's death, in general. Harry loses the closest he's ever had to a father, and it's all his fault. While Harry loses a lot of mentor figures over the course of the series, Sirius is the first (other than his parents, who died in the past) and the one he was closet to.
A subtle one right out of the gate, with Harry brooding alone at a playground and watching a mother and son leaving the park. And Harry just stares at the empty roundabout and you know that he's thinking about, among other things, how much he misses his own mother and how he never got to have moments like that. Then Dudley shows up with his gang and reminds him as much.
The scene where Umbridge fires Trelawney. "Hogwarts is my home!"
One can only imagine that Harry, who felt the same way about Hogwarts and, for a few short moments the previous summer, was actually expelled from the place, actually sympathized with Trelawney for once.
Hermione's reaction. She always seemed indifferent about Trelawney, not really taking her seriously. But like Harry, she actually feels bad for the woman.
Umbridge is already a vile piece of work, but in the film, it is revealed she uses her quill on little kids, saying "naughty children deserve to be punished."
One of the most memorable parts is Harry and Luna in the forest with the Thestrals. If you've ever been ousted from peer groups for being odd or different, this scene hits very close to home.
Luna: They're called Thestrals. They're quite gentle, really, but people avoid them, because they're a bit...
Made even sadder when the only reason that Harry and Luna can see the Thestrals, because Harry couldn't at first, is because they've seen death. Insert flashback of the previous film's climactic scene and aftermath.
In other words, Luna watched her mother die. Said death was also implied to not have been pretty. At all. In Luna's own words, "It was quite horrible."
Luna is also barefoot in this scene. She says it's because all her shoes have disappeared, and that she suspects Nargles are behind it, but maybe it's because she likes being barefoot.
Previously, we had only seen bits of Sirius's damage from his stay in Azkaban, and that was mostly the screaming newspaper photo and how he acted after he met up with his old friends in the Shrieking Shack. This shows that the scars and damage are much deeper.
When Sirius tells Harry that, when the war is over, they can finally be a proper family. A Heartwarming Moment, yes, but also a Tearjerker because Sirius dies before they can. The next time they meet, in fact.
Sirius's death. Even for those who don't cry very often at films, this was absolutely devastating.
Sirius: Nice one, James!
Hagrid's plea to the Trio to look after Grawp for him. He's such a big softy.
Grawp's face after Hermoine demands to be put down. He looks hurt.
The scene where Fred and George sit down to comfort a crying first-year after he's been punished. They show him their hands and say, "See, it's not so bad. You can hardly see the scars." Despite being comedic characters, they're also good men, protecting and comforting the weak when they need it. And that's why the two slacker jokesters are Gryffindors.
The utter despondency and grief in Remus's face when Sirius gets killed.
And Harry's absolute anguish during this scene is heartbreaking. After Sirius goes through the arch, the score starts playing over the scene so that you don't hear any of the character's voices. But then you see Harry stare at the arch in horror and say "No!" Then it cuts to him screaming in agony as Lupin tries to calm him down. You really do want to see Bellatrix get her comeuppance as she gleefully sings "I killed Sirius Black!". It even provides the image for the main page.
And the worst part was that Daniel Radcliffe wasn't miming that scream. The reason you don't hear any audio at that moment was because they cut it during post-production. Apparently, it was too agonizing.
Dumbledore trying to reach Harry through Voldemort's possession of the latter, stunned and near tears with a real look of concern on his face.