I have found that the best way to deal with games like that is to just be prepared. I know it's coming, so every time I turn a corner, I have got sights up to my shoulder if it's possible (use zoom in FEAR, use the scope on the SMG in Quake IV) and simply make sure I use "SWAT turns" (ie. go on one side of the doorway, use the flashlight to check one side, once that's clear, switch to the other side, check that area. If it's all clear, I'll move past the frame with my weapon ready to fire.
My first instinct when I get the **** scared out of me in a game is to shoot like a madman, and it typically works. Doom III was tougher to stomach with its ambience noises and the grinding of the industrial machines and grating of the steel in the background.
I don't really get actually frightened easily, but when something jumps out at me from the dark I nearly shat my pants. Some people enjoy it, I don't particularly, so if I'm in a situation where it's necessary, I'll do all I can to be methodical about it and prepare myself. The Doom III strategy guide helps a lot as it tells you the exact location of all the enemies.