I'm not aware of a glossary anywhere that defines all the possible types of required crew, but I can name some.
The important thing is that the definition of "required crew" varies based on the requirements of the flight, not the certification of the aircraft. Required crew are also those crew required to safely operate the aircraft under the conditions of the flight. For instance, a photographer (who has no other duties) is not "required" crew even if the purpose of the flight is to conduct photography.
First you have the crew required by FAA regulations:
Obviously, the pilot, and co-pilot if required. Along the same lines, an instructor, safety pilot, or examiner would also be considered required crew if required by the flight (if the pilot is not rated in the aircraft, or is wearing a view limiter, etc.) Also, relief pilots, if the duration of the flight is long enough.
Navigators and flight engineers, although few aircraft still need engineers and navigators are basically obsolete now.
Flight attendants, if the aircraft carries more than nine passengers.
If the aircraft is carrying hazardous materials, then a cargo specialist might be required.
Where the definition of "required" and "crew" gets a little sloppy is when it comes to experimental aircraft. If the aircraft is something like a new airliner prototype, then the engineers will have produced a mountain of paperwork detailing exactly what the crewmembers are and what they need to do. But for amateur-built or ex-military aircraft, "required" is a bit more nebulous. One particular case is the Commemorative Air Force's B-29, which the CAF likes to fly with extra engineering crew that the USAF didn't use when they operated it:
The FAA isn't always thrilled about this, even where there's an engineering justification for it. An ad-hoc "emergency gear lever crewman" on what amounts to a pleasure ride would be one of those wink-and-nudge cases that, if the flight actually experienced a problem, would probably incur some ill will from the FAA or NTSB investigators.
Anecdotally, I've also heard of amateur-built aircraft taking up two crew on testing flights, one to fly the plane and another as, essentially, a flight engineer, especially if the engine being used is not an ordinary Lycoming/Continental.
In the US, regulations restrict the use of the jump seats only to approved persons, such as a relief pilot, company check pilot, or someone else who "belongs there."