Here's one I'm real happy to see someone mention. Absolutely deserves to be remembered as one of the great short horror games, alongside PT.Anatomy
The first of a set of obscure games on my list, Anatomy is a $2.99, indie, minimalist game by the solo creator, Kitty Horrorshow. It's also, by far, the scariest game on this list. You're dropped into a house. It's dark. Very dark. You're alone. You come across a tape recorder, and a tape. You pop it in and listen. You're left to explore the house. I don't want to give much away, but Anatomy is an extremely tense, frightening game. It's deeply unsettling, and also extremely melancholic. This is on the artsier end of the spectrum, and if you enjoy this game, feel free to give Kitty Horrorshow's other games a look. They're shorter, and free.
And since I didn't do honorable mentions of my own, I'll also say people should check out My Father's Long, Long Legs and The Uncle Who Works for Nintendo, 2 free text-based horror games that are pretty short but very affecting.