Every year Stack Overflow corporate does a big survey of main site users. This year's survey can be found here. We also have a meta question here asking whether our stack can get a similar survey. While there are no actual answers to that question yet, I suspect the answer will be no, since a survey for the RPG stack won't provide nearly the same value to SO corporate that the SO survey does.
That doesn't mean we can't have a survey, though! It's not hard to make a survey for free on Survey Monkey, Google Forms, or other similar websites. The real question is whether the community really wants to do that, which is what this meta question exists to determine. If we seem to have consensus in favor of making a survey, we can use this question to hammer out exactly what we would want to ask.
To clarify, I created this question so that we have a place to discuss whether we should have a survey since the other question is unlikely to go anywhere. If I decide to argue in favor of a survey, I'll make an answer on this question laying out the case in favor of one.
Addenda: Making a survey is fairly easy once it's been decided what questions should be on it; I don't mind doing it myself if nobody else steps up.