Call of Cthulhu. In no particular order;
When you first encounter the Shoggoth.
When you run across a grating in the sewers. A corpse is thrown down. You who've played the game know what happens next.
When you nose about in the old newspaper building, only to turn a corner and get a close-up of a corpse that's been hanging there well past it's prime.
When you're trying to escape the Deep Ones on the boat.
Fighting Dagon on the boat.

1. Doom, the first one. Had plenty of legit scary moments that really made you jump.
2. X-Com: UFO Defense. Two different kinds of scares stood out the most, but this was a legitimately scary game. First is the farmhouse at night scenarios. You never knew where the aliens were, and the atmosphere was very tense in the dark. Suddenly BLAM the flash of an alien lit up by the fire of his gun - holy crap! Second was the zombie making alien appearing and turning one after the other citizens into zombies and then zombie making machines, blur fast, in one turn. Yipe! Nooooooooooooo!!!

Hexen 1
Death trap dungeon. This game is totally insane.

1.Thief: the dark project. First time I played crags cliff prison, I got scared at the zombies that I couldn't kill. The cathedral levels had me really scared because you had to be careful not to disturb the hammerite haunts other wise they would chase you down.
a. A glitch in the game where I was leaning around a corner to see what was there only to be sent flying into a wall and died.
B. I was hiding in the shadows and I didn't realize I was in a zombies path who was walking up beside me. Died
C. Random glitch in the fourth level when i was checking out a fireplace and I suddenly died for no reason. nobody or anything dangerous was there.
2. Resident Evil 4- The village attack. I got hold up in a corner of one of the houses with nothing but a knife.Managed to survive luckily.
3. Condemned- Any part of the game. Mad hobo's would manage to sneak up behind me or surprise me in strange places.
4. Thief 3: The Cradle. Just plain creepy. Plus I got surprised by a puppet that ran upstairs after me. I made sure he would go boom.
5.Spiderman for the Sega genesis. There was this glitch where if you stayed in Parker's room for to long he would take off his clothes and look like a demon. Happened once when I was a kid and I was scared to death. Don't know if it is replicable.

Aliens Vs Predator. The sound of a facehugger crawling around.
Sounds like you were a victim of sudden heart attack syndrome. Not really random, it happens when you crouch and creep across cracks, edges, etc. The broken stairs in Return To The Cathedral where the ghost of Murus hangs out are downright lethal as a result. There are some planks in the entrance of The Bonehoard that can cause it fairly consistently too.

I've also had a few jumps in Fallout 3, but its usually because I've been far to brazen with running about in dark underground locations. You'd expect that the Feral Ghouls give the most jumps, but for me it was the wasteland dogs and Yao Guai.
I was just minding my own business in minefield when one of those cheeky mofos snuck up on me while I was looking around ontop of a pile of rubble. I nearly jumped out of my chair when I heard it snarl and bite me. I was peacfully watching the sun go down as well. That thing ruined the moment.
Yao Guai just seemed to always managed to get the drop on me at night, I don't know why, but they were always too close for me to do anything other than panic. I was haemorrhaging bottlecap mines, which more often than not blew my legs off rather than killing the thing.

I remember once I was wandering around pretty aimlessly, just hitting any landmark which popped up on my hud when Ihear the sound of some form of wildlife behind me. I turned around thinking it was a dog or a mole rat only to be face to face with a deathclaw. Needless to say I nearly fell backwards in my chair while screaming. Sometimes I think creatures were designed to spawn behind you in that game.
Good times...

Strange no one mentioned STALKER. When you first encounter the Bloodsucker, the experience is incredible. They just come out of nowhere, creating genuine scares and a fear of proceeding forward. Then of course there's the Controller, whose roaring sound and sudden zooming into the face is really creepy. Poltergeists are also very creepy.
But of course, nothing beats the damn Bloodsuckers.

I could mention a few, like the orphanage in Thief, or the Ocean house from Vampire:Bloodlines (though that part is pretty much stolen right off 'the Shining', it's very well executed). The first time I saw the father in the boiler room I freaked out and had to call a friend who had finished that episode already, under the guise of him "helping me finish it". Yes. I had to call a friend.
There's actually one other game that completely scared me senseless, though I doubt anyone of you will have even heard of it. It was back in the mid 90's before the IT-bubble burst, and EVERYONE and their mother was making games. You know, back when they called it Multimedia. In 1997, ARLA, a Swedish-Danish dairy industry, commisioned some obscure studio to make a game for them, a game that was supposed to create interest in the company, the life of a (modern) dairy farmer, and to spur PR and goodwill.
It was called "Myulk". (Pronounciation is similar to the swedish word for Milk, and this twisting of the word already heralded the things to come)
It was terrifying. The player inherits an old run-down dairy farm and has three years to make it profitable. The latter part of the game is simple, but decent enough management. The problem is the first part, the "adventure-mode". This first part of the game has Myst-like graphics and interface, and you explore an abandoned farm, overgrown with strange black weeds, while ominous weather rolls overhead. This part of the game is smock-full of horror-movie elements, like when you look through a telescope and something suddenly appears very close in the viewfinder, followed by an unhuman laughter. Keep in mind this game was aimed for people about the age of 7-14. It turns out that the farm has been taken over by (yes I'm serious) an evil root with the name of Slymmer, and you must fight him to regain control of the farm. The music, and the atmosphere of this game chilled me to my core when I was a kid, and when I found it online a few months ago, I was shocked by how scary it was still. More than anything else though, I have never before or since felt so alone in a game...you know, almost alone. The worst kind, made painfully clear by the sign at the bus-stop: "The bus arrives in five hours".

It would be strange, if it were true.
The first bloodsucker was good, but for me, a lot of the scary came from not knowing exactly what it was. It really loses a lot on replay.
For consistent creepification, nothing beats that abandoned village by the military warehouses. For best results, go at night. During a thunderstorm.
Snorks also give me the jibblies. I don't like going to Yantar. Not until I get my hands on that semi-automatic shotgun anyway.

This is probably more of a 'woah I'm in over my head' rather than a scare but in Neverwinter Nights: Hordes Of The Underdark, I was playing a fighter/weaponmaster with a focus on the katana. My character was death on legs, she dual weilded a +9 and +10 katana with bucketloads of awesome effects (that forge was brilliant!) and she did criticals on I think an 8 or better so she was carving through monsters without breaking a sweat, triple figure damage almost all the time.
Then came the end battle where I met the Big M. A hit, 7 damage.
Err 7? Nah must have been 70 something, there's a lot going on at the moment & I misread it
Another hit, 2 damage.
2? 200 surely?!?
Another hit, 1 damage
Oh shit, I'm not going to win this one am I?
I was beginning to worry that I'd never finish the game thats for damned sure