Please don't list this on a work's page as a trope. Examples can go on the work's YMMV tab.
Tear Jerker: Amnesia: The Dark Descent
Believe it or not, Amnesia has one with the Valentine's Day custom story A Visit to Katherine. There are no monsters, no sanity to deal with, just you having to find recordings of your character's wife after waking up in the bedroom. As you play, you learn that your wife has fallen seriously ill and that you have some form of anterograde amnesia (you can't form new memories meaning your mind resets every day) AND retrograde amnesia so you can't remember your past either. Once you find last recording, when your wife says goodbye after reminding you of the day they met and the anniversaries they had, you enter the garden. And the last thing you see in the game is your wife's grave. Add superlative voice acting and you got a custom story that made Cry Plays, well, cry.
In the storage area you hear many flashbacks where a little girl is fleeing from her pursuer. That would be Daniel after going over the edge. Her dialogue is mostly screaming at her attacker to leave her be, but one sad line sticks out in this troper's mind. "Please let me go! I won't tell anyone, I swear! I just want to go home..."
Daniel's confession is a very emotional moment from the game too.
Alois' Undying Loyalty to Justine tends to envoke sympathy from many fans. It's helped by the fact if he kills Justine he says, "Hush now... It's all right..." After everything she did, he still loves and forgives her.