It varies by state. It varies by education level (engineering degree vs engineering tech degree, ABET accredited school vs not, etc). It varies by experience level (2 years of experience vs 20 years of experience).
There are so many factors that go into it, I don't think we can really give you a clean answer!
I don't think I can just give you a list of states that grant PE licenses without examination. Because anyone that has not taken the PE exam would have to plead their case to a given state to show that they have satisfactory education and experience to be licnesed. And those education and experience requirements vary by state to such a degree that you can't just say "State X gives out PE licenses without requiring an exam." Because even if state X did that for one person, it doesn't mean they'd do it for another person.
Pretty sure there is no way to get PE without passing the exam. Some states allow waiving of FE with 8+ years of experience. But all states are different, and you might have to do some research to figure out your best bet.
Like others have mentioned, you will have to talk to individual boards where you are interested in being licensed. Some states will allow you to waive if your primary employment is instructing courses in a university. If you plan to practice and stamp actual drawings i don't think that applies