Given that they live in a world torn apart by war, threatened by unimaginable horrors and rife with an all-too-casual attitude towards sibling-sex, it's probably little wonder that a few key characters aren't exactly of sound mind.
Living in what is essentially a medieval society, these guys probably don't have access to the creme de la creme of psychiatric care. Given that they live in a culture in which sex, death, and violence are far more normalised from a much earlier age, and brutality is basically a way of life, perhaps it even pays off to have a touch of the psychopath about you.
But, with the gifts of modern psychology, and a great deal of oversight, we can dole out diagnoses for all our favourite GoT characters. Just what is Cersei's problem? Is Arya a badass or just a severely disturbed child? What are the true consequences of so resolutely "keeping it in the family"?
Obviously, it's not recommended that you use this article to diagnose yourself or anybody else with a psychiatric disorder (unless they're fictional, of course, in which case carry on), leave that to somebody with a certificate on their wall.