As the OP predicted, mine was Amnesia. It was the first game I played that I truly considered to be of the "horror" genre, Dead Space being more like a really neat third person shooter with a nice atmosphere that would startle me now and again.
I was mildly tense for a while in the early sequences of Amnesia, but not particularly scared, as such (scared being that full-body fight-or-flight response with excess tension in the chest). What really did it for me was the first appearance of the invisible water monster.
On a side note though, on my second playthrough of Amnesia the water monster was VASTLY less scary than the first time. Once you fully comprehend something, its scare factor decreases.
But the first time? Yeah. I was freaking out, at least in the confines of my head. I find it much easier to be afraid of a creature that leaves a lot to the imagination, and as it was my first playthrough I had no idea what the rules of engagement were as yet. For all I knew if I stood too long on a box, it would jump up and get me. And I had to figure out how I was supposed to get past it.
I would call it my first true psychological "horror" experience in a game. It was refreshing.