Finite State Machines (FSMs) are one of the simplest AI model forms and are commonly used in the majority of games. A state machine consists of a finite number of states that are connected in a graph by the transitions between them. A game entity starts with an initial state and then looks out for the events and rules that will trigger a transition to another state. A game entity can only be in exactly one state at any given time.
For example, let's take a look at an AI guard character in a typical shooting game. Its states could be as simple as patrolling, chasing, and shooting: