In video games, psychopaths are characters who have mentally broken down to a state where they are incapable of rational thought, and this state leads to random acts of violence against the player. Dead Rising prominently featured psychopaths: the Zombie outbreak in the city of Willamette caused several survivors to become psychopathic. These psychopaths have an irrational rage that makes them act aggressively. In Dead Rising, the psychopaths act as bosses, and they must be defeated in order to save regular survivors as well as to gain experience for the player character - Frank West. In order to make the psychopaths more deadly, they are often given powerful weapons, new abilities, and extended health bars. In Dead Rising, psychopaths must be killed in order to progress through the game.
In Bioshock, the people of Rapture have turned Psychopathic as a result of excessive misuse of genetic enhancement drugs called Plasmids. Plasmid misuse has turned them into beings called Splicers, and they demonstrate psychopathic behaviour in their desperate search for a strange substance called Adam.
Not to be confused with Sociopath (though the two do overlap sometimes).