You might think of the movie Conspiracy Theory, but that's not exactly what I had in mind. While some degree of paranoia would be a good feature, the protagonist I'm suggesting would exercise more self-control. The hero's madness would take a more sporadic, more hallucinogenic form that the player could feel. Here are some examples, from my comment on Trent's post:
Schizophrenia runs in my family. For my cousin, hallucinations have taken the form of believing others are angry and yelling at him when they are not. In a game, experiences like that could be used to make a player unable to discern who can be trusted, who are enemies and allies.The basic idea is a character who can carry on a very clear and orderly conversation but occasionally falls victim to delusions and problems such as these. These problems could make him distrustful of others, make other distrustful of him (when he's telling the truth), and affect the player's interaction with the environment.
I have much milder schizophrenia. I've had hallucinations where my mind couldn't organize the patterns I was seeing into a meaningful image, so I saw one thing as something else. In gameplay, the player might see something falsely the first time and correctly every time after that, creating the possibility that the player bypasses something useful. Imagine fighting with a baseball bat and realizing halfway through the fight there's a gun nearby.
I've also had memory blocks. A few years ago, I asked my brother how he got the eggs in the frying pan to be all yellow. For about 5 minutes, the very mundane memory of eggs was trapped in my mind and everyone was looking at me like I was crazy. That frustration of hearing everyone around you identify reality as something other than what you're seeing it as... that's gameplay I haven't seen yet. It could be compelling gameplay if the character also saw some things differently than other people and was correct in those observations. Imagine a schizophrenic hero working to unravel a true conspiracy.
The visual delusions might even be used to create an adaptive AI that adjusts difficulty to performance, ala Left 4 Dead. The more help the player needs, the clearer the character's perception becomes, opening up new opportunities.
There are other schizo symptoms that might play a role, such as being aloof or having trouble finishing more than a couple sentences without a pause or wandering thought. But, in any case, my point is that an unreliable "narrator" and conspiracy could be a great mix.