This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Dead Poets Society
Expect unmarked spoilers. Best if you read this page after you have seen the movie.
As Professor Keating leaves his classroom for the last time after the school fires him for Neil's suicide, the remaining members of the Dead Poet's Society all stand on their desk, look at him, and say "Oh, Captain, my Captain!". There were even members of the class who WEREN'T members of the Society, meaning that it wasn't JUST the DPS that took Keating's message to heart. Total heartwarming.
Todd after learning of Neil's death, walking in the snow, looking around and commenting on the beauty of it... before practically vomiting with grief and then charging away across the field screaming Neil's name.
When Keating sits at the desk that had been Neil's and flips through the book that he himself used as a member of the Dead Poets Society, he eventually breaks down and starts weeping.
Neil's sadness when his father tells him "I don't care if the world ends tomorrow night, you are through with that play!" Topped only by his suicide. While his father is clearly having an It's All About Me moment, his mother looks genuinely distraught.
When Neil's father has just finished chewing him out, and Neil is sitting with his mother. He has a completely spaced-out and in-the-clouds look on his face as he says, "I was really great, wasn't I?"
If you look really closely at Neil's father after the play, when he's berating Neil about wanting to be an actor and asks him why he wants to do it, he looks more frustrated than angry as if he really wants to know why. Which makes his reaction to Neil's suicide that more heart-wrenching, because you wonder if he wanted to fix his relationship with his son and now he's lost his chance.
Neil's mom screaming, "He's okay, he's okay!".
Neil's father turning up at the opening night for the play, waiting until it is done, then taking him back to their house without a word of congratulation. The others try to tell him that his son has done well, but Keating tells them dejectedly "don't make it worse than it already is". He obviously agrees with them, but is Genre Savvy enough to know it's too late.
A very subtle one occurs after Neil's death. At his memorial service at the school, the dead poets are seen in a line, singing wistfully. All except Charlie, who stares forward, angry and unmoving and silent.
The audio commentary says Keating blamed himself for Neil's suicide and fell into a deep depression, and without the boys standing up for him he might have never recovered.
With Robin Williams committing suicide in 2014, this movie just becomes even more of a tearjerker than it already was.