normally not for any US possession (e.g. pr, any states, a couple other places), but you do need ID for any flight and a passport will/always has been strong enough ID (for a time there were certain states that issued IDs that DHS didn't consider to be 'forgery proof enough' to be valid IDs for air travel)

Not to other states, but it does help at airports. Usually a driver's license is suffiecient. Even to go by car into Canada and Mexico, I believe that you need a passport now--every since 9-11...

Just out of the U.S.

You must have "picture" I.D. that is current and acceptable, passports are preferable, however...