I suppose applicability depends on the problem domain. In embedded systems that control some device I've found them very useful, particularly as the logic becomes complex. () Perhaps for other realms such as Web back ends that tend to be transactional, they are less useful.

() Many years ago I was tasked with coding a replacement for a device that operated from discrete logic involving a number of inputs, timers, decisions and actions based on all of these. The first thing I did was to model it as a state machine and everything went well except for one part where it was not clear what the next state should be based on the inputs. I reviewed this with an engineer familiar with the existing logic and he shared with me that the actual behavior of the device was indeterminate in that particular situation. That was easily fixed with the state machine.