Eleven-year-old Harry looking into the Mirror of Erised and seeing his dead family is a heartbreaking moment and somewhat iconic in terms of the series as a whole.
Dumbledore's claim that the Mirror shows himself with socks is hard to read after you've read Deathly Hallows and know what he really sees. The same as Harry does, his family, alive and well.
Chamber of Secrets
Ron and Harry's reactions to Hermione being petrified.
Hagrid being carted off to Azkaban for a crime he didn't commit. Doubles as Fridge Horror as the experience scares the crap out of a half-giant who thinks a giant, three headed dog is cute and a young dragon makes an adorable pet.
Professor McGonagall's heartbroken reaction to Hogwarts potentially having to close.
Definitely a subjective example, but it's pretty sad to see Filch's reaction when he discovers that Mrs. Norris has been petrified, especially in the film, where he sounds so extremely... broken.
Just like the scene in Goblet of Fire where Dumbledore explains to Harry what happened to Frank and Alice, and Harry himself is so appalled that he thinks he was lucky to just have his parents dead, whereas Neville's parents still live but can't even recognize their child, so damaged they were.
When Moody taught the Unforgivable Curses, it must have been having a hell of a moment for Harry and Neville...
It's actually both a Tear Jerker AND a Moral Event Horizon for Fake Moody. Think about it. HE is the one responsible for Alice & Frank's demise, along with the Lestranges. Now look at that scene again. He is basically torturing Neville for: A) His own ends, just to get a chance to revive his Lord, and B) Because he KNOWS how Neville would react.
Worse so in Harry Potter and the Order of the Phoenix when Harry, Hermione, Ginny, and Ron actually see Neville with his parents at St. Mungo's. Neville's grandmother tells him to throw away the wrapper Alice has given her son, and he slips it into his pocket. Anything with Neville and his parents, really.
God, that scene... somehow it's made even worse by the fact that, in the middle of this fantasy series with all sorts of funny spell effects and whimsical noodle incidents, we get a very low-key, realistic depiction of a son visiting his mentally shattered parents.
Just realizing that Harry won't be with Sirius in the end of Prisoner of Azkaban.
Any moment between Narcissa's betrayal of Voldemort and Voldemort's death. The two that give me the worst case of tears are Slughorn (who has always been shown as a bit of a coward) leading the reinforcements for the Battle of Hogwarts and Molly Weasley fighting with Bellatrix Lestrange.
The realisation that Andromeda Tonks lost her husband and her daughter's husband walked out on them. Then, he comes back, her grandson is named after her dead husband, and it seems okay. But then there's the battle at Hogwarts. Lupin leaves, and then so does her daughter, and neither of them come back, leaving her with her grandson, named for her husband, and with the same morphing abilities as her dead daughter. The woman barely appears in the book, but experiences as much loss as so many others. (Also, Sirius had died nearly two years beforehand, and a comment Sirius makes in Book 5 implies that they were closest to each other among their family members.)
Not to mention the fact that she's the sister of Voldemort's right-hand woman. You see Harry's reaction to her when he doesn't initially realize who she is (or rather, who she isn't), and wonder if other strangers had given her that same reaction. And then you wonder if that has anything to do with the fact that she and her husband live in a secluded location, away from other wizards and witches.
Barty Crouch Jr.'s story. His past is still depressing. He was the "Well Done, Son" Guy, with a father who loved work a great deal more than his own son. He did whatever he could to impress his father, who never let Barty know that he was impressed at his top grades in the OWLs and the NEWTs. The only family member who loved him died to give him freedom, which he never obtained because he spent the next thirteen years under the control of his father via Mind Rape, which drove him mad. He sided with Voldemort because he was more like a father than his own to him.
Ghosts are unable to move on from whatever they did in life. Moaning Myrtle is perpetually trapped in the mind of a suicidal teenager.
The Mirror of Erised scene in the first movie, particularly the point when Harry reaches out to the image in the mirror and realizes that it's only an illusion.
Chamber of Secrets
After Harry speaks to the snake during the duel all his classmates think he's an evil freak. It only furthers the rumor that he is the heir of Slytherin, a rumor he isn't even sure is false. He's a twelve year old boy and something he didn't even know about himself is now isolating him from people he considered to be friends.
Ron and Harry separated from their best friend (and in Ron's case, burgeoning love) for months. Not to mention that Hermionie is already established as the brains of the operation, leaving them even more scared and desperate.
An example in Real Life: The London Premiere of the final Harry Potter movie, Deathly Hallows Part Two at Trafalgar Square packed with thousands of fans. Each of the trio making a speech with Emma Watson crying and Rupert telling the other two "I love you" and an emotional JK Rowling thanking the fans and saying "Whether you come back by page or by the big screen, Hogwarts will always be there to welcome you home."
Or when Emma tells Rupert: "Thank you for being such a good brother."
Wrock (Wizard-rock) has a few songs about Harry walking to his death, but The Butterbeer Experience's Chapter 34 tops all. "I know what I must do. And I am prepared. But, please stay here, so I'm not scared. No time to explain. No time for goodbyes. Only time for tears as I look into your eyes. So, hold my hand. Touch my heart. Know that really soon, I'll be where you are. I'll face him strong. Just . . . stay by my side. I want you there, when I, when I die."
Made worse when Lena, who's still singing, just breaks down and starts crying.
On that note, Riddle TM has a song of the same name that is equally heartbreaking- it's softer, mellower than TBE's Chapter 34... " I hold the ring in my hand, Iíll be okay now I have the bitter truth at last.Help me through, strengthen my resolve Help me face Voldemort, With courage and without fear...."
Oliver Boyd and the Rememberalls's Chapter 34 song, Open at the Close, has a heart breaking chorus: "So I'll walk it alone and face this truth. Mum, I'm coming home, home to you. No goodbyes this time, and no kisses too. Ginny, please don't you cry. Know I'll always love you." *sob*
A lot of TBE's songs are sad, but the crown goes to "The Prince's Tale"...
Oliver Boyd and the Remembralls 'End of an Era'. Really that entire song, but to be specific: "I will miss the train ride in, and the pranks pulled by the twins. And though it's nowhere I have been, I'll keep on smiling from the times we had with them."
The Split Seven Ways song "The Forest Again."
The end of the Epilogue. It wasn't the end of the movie, no, it was the damn song. The very same song that played at the very end of the first movie. It told us, really, everything ran full circle. It reminded us of the entire scope and tragedy of the whole series compered to the first book.
"The scar had not pained Harry for nineteen years. All was well." It was like that feeling after you've gone through a long ordeal and it's all over and after so much time trying to hold it together, you just need a shoulder to cry on. And it wasn't just because the story had ended - it was the feeling of closure for a character that really, really had to earnthat happy ending. And it was the implication that his horrible childhood and seven (some would argue seventeen)-year struggle with Voldemort had left no lasting damage. He didn't end up going off the deep end. He didn't suffer from waking up in occasional cold sweats with hell itself exploding out of his forehead. He didn't have any worry about whether a fragment of Voldemort's soul would come bursting out of him at any moment to endanger the ones he loved. He grew into a man, married the one he loved (a miracle in and of itself considering her proximity to the violence), and had three healthy, happy children as well as a host of nieces and nephews, achieved his career goal - and then some note He wanted to be an auror. He ended up becoming head of the entire freaking office - at 27!. And they all lived Happily Ever After. That's essentially what the last sentence says, but more beautiful - more poignant.
"Richard was by my side during two of the most important moments of my career. In August 2000, before official production had even begun on Potter, we filmed a shot outside the Dursleys, which was my first ever shot as Harry. I was nervous and he made me feel at ease. Seven years later, we embarked on Equus together. It was my first time doing a play but, terrified as I was, his encouragement, tutelage and humour made it a joy. Any room he walked into was made twice as funny and twice as clever just by his presence. I am proud to say I knew him."