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My opinion is that as long as you put in the time to make them good questions (try browsing the closed questions to get a sense of what is not good), they are appropriate for the site. I think Critch's question http://mathoverflow.net/questions/2985/derived-functors-vs-universal-delta-functors is a good example.
I think you're much be better thinking about a couple of specific questions than trying to guess in advance whether they will be appropriate. Then search on MO to see whether there has been something similar in spirit. If you don't find, just post and let the community express its opinion.
Since you are unsure, invest a bit more into writing correctly, putting links, using good structure. And say you've already read Wikipedia and did Google. That dramatically highers the chances people will like your question.
MO is very much meant to handle those sorts of questions. You shouldn't feel bad about them or believe that you need to tag them in a special way so that others can ignore them. But you should try to provide some background and motivation and make the question interesting to others. The thread Harry pointed to is a good example of how to take some bit of a proof you're stuck on and turn it into a question that has much more appeal than "Help me work through this proof".
I hope to have a preliminary draft of a guide to asking good questions up soon. The basic idea is that asking a question on MO should be an extension of how you normally solve problems in mathematics. Suppose you're studying for quals and you hit a snag; either you don't understand a result or you don't know how to do a problem. Try to break your problem down into smaller pieces ("if there's a problem you can't solve, there's a simpler one you can't solve") and ask it to yourself from different points of view (e.g. instead of asking, "where does the proof use X?" try "is the result true without X?"; instead of trying to prove a result, look for counterexamples). Chances are that you'll either resolve your problem (great!) or reduce it to a question that is interesting by itself which you can post on MO (in the case Harry linked to, "Is every left fibration of simplicial sets a trivial Kan fibration?").
@fedja: Yes, I seriously mean that, but I think you're misunderstanding what I mean by those words. If somebody is stuck on something, I don't think he should post to MO, "I'm stuck while trying to do X, how do I get unstuck?" That is the real question he's trying to solve, clearly stated, but it's a boring one. Instead, he should ask himself "why do I want to do X?" and "why might somebody else want to do X?" The answers he comes up with should go into his question as "background and motivation". Moreover, he should break X down into smaller problems if possible. Perhaps accomplishing X is a matter of doing Y and Z. Actually, maybe he can already do Z, so he just needs to figure out how to do Y. But really Y might have a natural generalization W which is probably interesting by itself. After going through this process of breaking down and recontextualizing the problem, he can post an interesting question: "Is W true?" or, depending on what W is, "Is there an example of (not W)?" Explaining that he's trying to do X and that he thinks proving W is the right way to do it should also go under "background and motivation" if it's not too far removed.
I don't think the we should tolerate questions that offend the sensibilities of members of the community. MO is not meant to be a way for non-mathematicians to get better access to mathematicians; it's meant to be a way for mathematicians to get better access to each other. I agree that there's a place for PR, but I'm far more concerned with keeping mathematicians interested in visiting the site than I am with making the site friendly to non-mathematicians.
@fedja: I assume your last comment is directed entirely at Harry and not at me, but just in case, let me clarify. I have no problem with non-mathematicians on MO, so long as they play by the rules. Namely, they should ask questions that the community finds interesting. A question does not need to be hard in order to be interesting. In fact, MO is very much meant to help resolve problems that somebody probably knows the answer to off they top of their head.
Harry, fedja- This is not really a productive discussion, so i hope we can all agree to end it. It sounds to me like you are talking past each other. I don't care if a question is written by a dog, if it is good, so let's not have any discussion of who we should have on MO, but what we want on the site. But certainly good writing is part of what we want on the site, and it's important that Q-and-A writers understand this, especially if they want good feedback.
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