I find UML state diagrams useful for specific, localized bits of projects where it is not necessarily possible to hold the entire state machine in my mind while developing/interpreting the code. It acts as a spec to guide writing tests and tells future visitors to the codebase exactly what I was trying to do. I check the UML diagram into source control alongside the code, which contains comments pointing to the UML diagram.

The key is to use this sauce in limited amounts and only to guide the development of truly critical parts of your code. A utility library to convert dates? Eh. A core library that handles complex multiparty bid management for a market? Definitely.