There have been a few games that startled me, namely Far Cry, Call of Duty, and the Half Life twins.
As for actual anxious fear, only one, Delta Force Extreme.
That sounds odd, so let me explain. In multiplayer they have helocopters, and on a cetain map I found that I could hide in the grass, wait for a enemy to start winding up thier gunship, then run out (shooting the pilot) and steal the chopper.
The fear set in as I lay there, hopeing they don't see me, while knowing that if I went too soon then the helo wouldn't be ready and I would be gunned down as I tried to get it off the ground; or that I would run out too late, in which case it would fly away and I would be stuck in thier base with everyone looking at me.
Real fear isn't being spooked, it's in the tension of things.