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Tear Jerker: DRAMAtical Murder
The bad endings. Though some of them can also enter the terrifying category.
The main characters' backstories.
In Noiz's Route, he becomes brainwashed and Aoba has to use Scrap on him. While we're in his head, we overhear his parents talking—and one says that it would have been a blessing if he had never been born, and they both admit that they aren't planning to let him out of his room. This was all within earshot for Noiz as a child.
When Noiz is describing his backstory, there's some of this, along with some heartwarming. Possibly his saddest line is when he's nonchalantly talking about his childhood locked in his room: "At first, I was so lonely that I cried." Seeing as all we've seen of him has been him being stoic, this puts everything else into perspective...and makes it all heartbreaking.
Clear's Disney Death, which also includes his and Aoba's sex scene, which is absolutely heartbreaking.