Sorry to revive an old thread but I was going to start a new one with exactly the same topic so I thought it made sense to reply here.
I had a few games that scared the shit outta me on the Amiga, I was about 8when I played these titles too! Games didn't have age ratings on back then, kinda wrong really considering some of the graphic gore in the games. The games that stand out are:
Personal Nightmare (The whole atmosphere in this game was terrifying, the fact that if you were in the wrong place at the wrong time you would get killed without warning was unsettling. The Screens that followed your death were also some of the goriest images I ever saw on the Amiga)
Weird Dreams (Another seriously twisted game, it wasn't so much the gore that was scary, more the storyline itself and the sheer weirdness of each screen. Also the sound effects, music and surgeon screens when you died were quite haunting)
It Came From The Desert (MUSIC!! That was what made this game scary! The storyline was more sci-fi than horror I guess but the atmosphere was intense due to the in game music and sound effects. Trust me, play this one with the lights off!)
There the ones I remember off the top of my head.