System Shock 2 had tons of atmosphere & was scary as hell.

F.E.A.R. is quite scary, in more than one way... it has a way of combining the subtle terror with the "jump-on-your-face" terror quite well. I know I had a couple of chill-down-my-spine moments with it.
Operation Flashpoint can be a terrifying experience, in a very different way. There are a few missions where you feel the terror of being all alone in the woods trying to find your way out through dozens of patrols, or hearing an enemy tank approaching when you're infantry. There's even a "guard" mission, at night, which is particularly tense - one I'll never forget.

Some games, ie. Doom 3 made me jump in my chair but were not actually that scary.
Aliens vs Predator 2 was the first game I was genuinely scared while playing. Most FPS games cast you as a super soldier of some kind, able to kake down thousands of enemies.
As a marine in AvP, the game does an amazing job of making you realise just how vulerable you are to the Aliens and Predators.

The only game to genuinely scare me is Project Zero/Fatal Frame.
I've played Silent Hill, Doom, Resident Evil, System/Bio Shock, Call of Cthulhu, The Suffering etc. But Project Zero/Fatal Frame is the one that had me scared.

The last game which really scared me was F.E.A.R and maybe Stalker Shadow of Chernobyl too but only a lil bit.:p

Descent 2, with the darker corridors and more robots that scraped against the manifold of your ship. There were many a time when I wasn't paying attention and the horrific metal wrenching noise made me jump in my seat.

System Shock 2 - no question about it! I remember the enemies yelling "kill meeee".. and I was playing hard.. I was really scared, didn't wanna die. And I also played at night with headphones. lol.
Ultime Online - The first time a player killer chased me. I was poor and didn't want to lose my armor. I ran for my life.. :)
Also the first Alone in the dark game.. it was a bit hard to play due to the fixed camera perspectives, but at the same time that effectively managed to scared the hell out of me.

Wolfenstien 3D gave me nightmares when I was a kid probably 8 or 9 (mostly the zombie episode: or whatever those things were with guns in their chests)
When I was a freshman in high school I played the demo for Clive Barkers Undying and looking at the pictures on the wall change gave me and my friend the willies so we stopped playing and never did buy the game although we looked for it later.
but yeah other games that have startled me more then once were
Half Life (the second one didn't seem to make me jump like the first one did)
F.E.A.R. (My cell phone was on vibrate and started ringing right when I turn around in this hallway and alma's walking toward me on the ceiling and the floor is on fire... Yiiiihhhh!!!)
Aliens vs Predator 1 & 2 (a friend owned it so I only got to play multi-player at his house, but he was really good at being an alien, scared the crap out of me all the time)

I played the demo for Undying once and I remember you see something move in a mirror, but if you turn around there's nothing there. Couple the freaky moments in the game with the fact that a thunderstorm started outside and I just quit the game and haven't touched it since.

original alone in the dark scared me when that low poly werewolf suddenly jumped through the window for the first time... ah, the memories.
the beginning of the first silent hill where you walk down the alley and get attacked without means to defend yourself was pretty hearstopping for me too.. playing alone in a completely dark house with a storm raging outside... didn't touch the game for days afterwards.

3 incidents come to my mind immediately:
1) My cousin and I were playing Morrowind: Game of the Year edition, and this was about two years ago, just one or two days after we just bought the game. It was about 10pm at night, both in the game and real-life, and I'm watching her play. She makes her character rest. Suddenly, she's awakened, and there's one of the Dark Brotherhood attacking her. Obviously, she freaks (her character's like half an hour old and has poor armor). Later, in her journal after she runs away, it told her that she was "targeted for assassination". As a bystander, I was howling with laughter, but that was pretty creepy.
2) For some odd and stupid reason (also accompanied by a long story), I decided to read the FAQ for the original Clock Tower game for SNES one day. (Or was it NES? I'm pretty sure it was SNES) You're basically a young girl trying to escape from a psycho scissor-wielding killer in a [literally] gothic mansion near a clock tower. I kept reading, because even though I was freaked out, somehow I wanted to know about the endings. In every ending, at least one protagonist died, and it was just...wow. Would make a great horror movie. I would never go see it, though.
3) When I tried the Half-Life demo and I got to Ravenholm. I played for about ten minutes and uninstalled the rest of the demo. I know, it wasn't even the real game.
So there are my chicken stories. Ironically enough, none of them involve me actually playing real horror games.

The first game that actually scared me was Resident Evil on the Playstation. It started off with quick jumps, like the dog-through-the-window, and eventually became unnerving as I got further ingame. The audio was done quite well. <_<;;
Another Playstation game was Doom, but not for its graphics, but its background "music", which was a collection of sounds and atmosphere, rather than any sort of tune. I eventually played the game with the BGM off, as I kept "hearing" it long after I shut off the game.... o_O
Silent Hill, also on the Playstation, was another scare-game, and System Shock 2, on the PC.... well, that particular game, which I never heard of at the time, didn't seem to mention anywhere on the box that it was anything other than a first-person shooter with RPG elements... in space.... >_<

Just wondering, has anyone ever played Thief: Deadly Shadows? The Shalebridge Cradle level is sort of scary in itself.
The laydown for those who haven't heard of it: An orphanage/mental asylum that supposedly burned down but it still stands in the middle of the city. People hear crying coming from the building every night.
The place scared me stiff plenty of times. The mental asylum patients walk all over the place; the Cradle is electrically lighted. Whenever an asylum patient comes near a light, it starts flashing. I've been scared out of my daylights many times over whilst trying to lockpick a door in the middle of the hallway.

American Mcgee's Alice.
Scared me so much when I was little.

The first game to scare me was AvP 2 I didn't play the original. But the Marine campaign scared me quite a bit going up against the aliens in dark corridors.
The most recent would have to be F.E.A.R. the original.