The State pattern is applicable to many problems. All the problems that can be solved using state machines are good use cases for using the State pattern. An example we have already seen is the process model for an operating/embedded system.
Programming language compiler implementation is another good example. Lexical and syntactic analysis can use states to build abstract syntax trees.
Event-driven systems are yet another example. In an event-driven system, the transition from one state to another triggers an event/message. Many computer games use this technique. For example, a monster might move from the guard state to the attack state when the main hero approaches it.
To quote Thomas Jaeger:
"The state design pattern allows for full encapsulation of an unlimited number of states on a context for easy maintenance and flexibility."