(Prompted by the discussion on this post.)
As a user-moderated question and answer site, the decision of what sorts of questions are and are not allowed is obviously up to the users themselves. However, since most user-moderation tasks require large amounts of karma to exercise, we are currently not at a stage where the users themselves have enough power to prevent abusive or off-topic posts from flooding the board.
As such, it is up to the designated Moderators (Al Ummat, NesreenA, Jenny_ and goldPseudo) to ensure the site remains viable until the userbase can build up enough karma and site experience to manage things in a more democratic fashion. One significant part of our duties is to ensure that posts follow the rules (as laid out in the FAQ).
It has been pointed out the the matter of deciding whether or not a question is "too subjective" is in and of itself subjective; what one Moderator decides is a problem could be seen as perfectly fine by another, and I agree with the concern this raises. Unlike the regular users, Moderators have the ability to unilaterally close and delete any post that they don't like. When the userbase develops to a point where it can handle the user-moderation tasks, this will not be as much a problem and the Moderators would only need to be called in to handle exceptional situations.
But right now, we're all you have.
Above all else, this is a site for the users. So I'm throwing this question out for both the Moderators and the users themselves.
Under what circumstances should the moderators use their powers to close questions?
Any new users to the site will be confronted by the front page of the site before they read the FAQ -- there is a very good chance they'll not bother to read the FAQ at all -- and they will judge what is or is not acceptable based on the posts they see. As such, it is important for the moderators to make sure that the front page is representative of how a new user is supposed to act.
If a new user sees argumentative posts, they'll instantly assume that argumentative posts are acceptable. If a new user sees "brainteaser" type questions, they'll instantly assume that brainteasers are acceptable. If a new user sees vague and subjective questions with no definite answer, again they'll assume such is acceptable.
If, however, they see any posts that are either closed or downvoted by the community, quickly and decisively, then they're likely to realize that such posts are not welcome here. Or at least know what to expect if they try to post the same.
If we want them to come in posting well-written questions with clear and precise answers, then that is what we should be showing them.
Discussing every decision to close with the other moderators is good in theory, but it relies on all moderators being reachable in a timely fashion; my personal take on this issue is that a moderator needs to be able to make snap decisions to keep the front page clear. In order to build a community of people who understand exactly what sort of question and answer site this is supposed to be, we need to take a hard hand and make sure that any new users that arrive see exactly what they're supposed to see; a Q&A site where "finding answers to existing questions - and getting answers to new questions - can be done without any distractions." (from the FAQ)
Sure, there might some mistakes; snap decisions are never foolproof. But closing questions is not the end of the world, a closed question can easily be reopened by another moderator or by any user with enough karma. And there's nothing stopping the original poster from reformulating the post as a new (and hopefully better) question, or even appealing the decision with a "Why was my question closed?"-type post.