I'll add a couple of games I haven't seen in this fun thread
One of, if not the first amiga game I witnessed was Moonstone. The swamp monster appears from out of the mud, accompanied by a loud shrieking sound, horrible arms spread out high ... then takes its victim (you) down under.
I refused to play that game for quite a while.
Another scary one for me was UFO: Enemy Unknown (UFO Defense in the US). Hearing it, but not knowing where the body snatching chryssalid is ... then seeing it round a corner just when you thought you were safe!
On the PC I got a few scary moments playing Lands of Lore. I'm not sure which version, but it was 3d, didn't have great graphics, and it was nicely dark and atmospheric. At one point, you walk down a dark corridor as it bends to the right. The screen turns black as your way is suddenly blocked, and a spooky voice whispers in warning: "BEHIND YOU!". I turned as fast as I could (still felt agonizingly slow... turn around, turn around!! aah!) and sure enough, some ghostly creature was walking toward me, already too close for comfort ...
I didn't see that kind of (scripted but effective) scariness until System Shock 2 and Half-Life.