I'm a big proponent of state machines. They are an excellent tool for unambiguously communicating how a certain critical part of a system should work - to that end, they are not only a coding tool but also a social one to get everyone on the same page. I've wandered several times into a situation where the state is not being well-handled and while it's not often loved, getting the team to hammer out a state machine does wonders for system reliability.
It's true that they have limitations and are not always the right tool, but it's often valuable to realize that you implicitly have a state machine already whether you wish you did or not.
Same here. I am a big proponent of state machines. I have found that state machines bring sanity to an otherwise complex situation. For example, most inexperienced developers will check presence of certain fields to imply where someone is in the process whereas it would be better written using a state machine.
It's true that they have limitations and are not always the right tool, but it's often valuable to realize that you implicitly have a state machine already whether you wish you did or not.