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Nightmare Fuel: Chulip
Let's start with the fact that the protagonist's health equivalent is more like a happiness meter. If anything upsetting happens — a dog barks at him, he sees a chicken being slaughtered, he finds one of the many sizes of poopie — he comes that much closer to a Game Over, and it doesn't take much in the early game. Certain activities restore happiness or at least give him an item that restore it, but some can only be done a small number of times per day to have any effect, and others have a random chance of an upsetting outcome (e.g. searching the trash might grant you a happiness-restoring Cold Sweet Potato... or it might get you Poopie). What does the Game Over screen imply? Death? Having to be committed to an insane asylum? Just lying there twitching while sentient inanimate objects come up and kick you? And how fragile is this boy?
Michelle. Michelle, Michelle, Michelle. At some point, whenever you talk to her, she looks directly at the player with this frightening look. And later, you find out her secret...
The police officer, particularly at night. Light shines from his eyes as he patrols Long Life Town, looking for curfew-breakers. His immediate reaction to seeing you out and about when he's on patrol? Shoot at you! Later in the game, your happiness reserves are big enough that the losses don't matter as much, but it's still pretty freaky.
Dr. Dandy. During the day, he can be found in his office, sleeping. At night, he roams the streets, looking for blood donations... which he takes by stabbing you with a giant syringe, withdrawing some into it, and drinking it! It's also pretty freaky when you cure him, but at least he stops doing that.
No surprise here: the Grim Reaper ghost (probably a Shinigami). If you're in Worldly Desire Temple's cemetery at night, it appears somewhere in there and moves toward you, unhindered by the gravestones that form a sort of maze. If it catches you, it swings its scythe, taking away some happiness. If you get caught again the same night, you lose an increased amount, and so on. If you're in the wrong place, it's very easy to lose with pretty much no hope of escape before the night ends.