I should start off by mentioning Oregon Trail, I suppose
When I was six or seven, I got so scared of my "people" dying, even though you can't see them and you just get a little message saying they died, I refused to play the game anymore or even watch my brother do it. It was too traumatizing
Another time was early in my first playthrough of ICO, before I knew how it worked. (This was shortly after you first meet Yorda.) I'd left Yorda behind to head off on my own to try to figure out how to move forward, but then I got too far away, and I heard her plaintive little gasp and the camera whipped over in that direction. But I was way too far away, so even though I started running back, heart pounding, I knew I couldn't get to her in time. And then that wave of darkness swept over me and it was Game Over, and that one incident got me so scared that I hardly ever let Yorda out of my sight after that.
There was a freaky part in Bioshock where suddenly the lights went out and I heard all these splicers rushing towards me, so I just started shooting wildly in all directions. Thank goodness I had the fire plasmid!
But the scariest experiences I've ever had have been in the game called Penumbra, which I've actually been too scared to finish ^^' It all takes place in this underground mine, it's very dimly lit, and they have such a realistic physics system that you're encouraged to react to the situations as though you're actually there. For example, in the demo of the game, I was walking down a corridor when a grate overhead suddenly fell open. There wasn't anything there, but it freaked me out so much that I immediately turned tail and ran to a closet and grabbed a broom to defend myself with, before I even stopped to think about it. And that's another thing - the complete lack of normal weapons makes this game absolutely the most terrifying game I've ever played. It's okay in most scary FPSs, because at least you have a machine gun in between you and the enemy. But in Penumbra, all you've got is like...a little hammer and whatever you can pick up around you.
Other scary moments have been a sudden scream overhead when everything had been quiet for a long time, then going upstairs to see a big bloody streak across the floor; the first time a rabid dog came running at me, snarling viciously and realistically; and whenever the creepy danger music starts playing, because it sounds like a heart pounding (to me) and makes me really tense.
There have been times in Penumbra when I've gasped really loudly or even cried aloud. Probably because I usually end up playing it when it's dark outside
Yup! I'm a coward when it comes to scary games. 
