It does vary a little by state.
My reading of the Washington State rules that I am familiar with gives me the impression that without an accredited Engineering degree, you could qualify to take the PE exam with 12 years of professional-level engineering experience, with at least 8 of those being under the supervision of a licensed PE and at least 4 of those being "independent judgement and decision making".
If you don't have a degree or the FE/EIT certificate, you can expect your work history to be carefully scrutinized by the licensing board.
For better or for worse, those are the rules. They probably keep some very skilled and experienced people from getting professionally licensed, and they probably allow the licensure of some world-class chowderheads. I know a few of both.