It would be a good idea to make your character have a strong personality, of course he should not be able to easily surmount the obstacles at hand, but it is alot more terrifying if it is a person with a strong will that is having to scramble to survive.
If the character is too weak, too weak willed, and too stupid, I do not really feel frightened when they get slaughtered, I just feel marginally surprised it did not happen sooner.
Clocktower on the SNES as previously mentioned actually accomplished this pretty well, sure she was a weak girl, but she was easily recognized as one of the stronger characters, by the other characters in the game too. She also had alot of willpower and was willing to push her body to the limit. The character should be feeling the same adrenaline the player is feeling or it is just pathetic.