We should get this moving, so I looked at a few other random sites' FAQ to get an idea about how this works:
I put some links here for your convenience.
One thing to notice is that usually the FAQ is modified only minimally: The first "What kind of questions can I ask here?" section is the most important, so we should take that first.
Here's a first draft (needs to be extended):
Mathematica.SE is for users of Mathematica. If you have a question about
solving problems using Mathematica {or related companion products such as Player Pro, Player or Wolfram Workbench}
Mathematica programming or the Mathematica language
the Mathematica user interface (notebooks, customizations)
then you are at the right place!
Please try to include short code samples with questions when appropriate.
Maybe this is already too specific, and we can just say
Mathematica.SE is for users of Mathematica. If you have a question about the Mahematica system or wish to solve a problem using Mathematica, then you have come to the right place!
Another thing which has not been said explicitly, but I think we agree on is that this site is not only for questions about Mathematica, but also about questions on how to solve certain problems in Mathematica. For example, my question about adaptive sampling is really a numerical methods question, but when phrased as "what is the best way to get this done given Mathematica's capabilities", I think it's on topic, even if I don't yet have the specific algorithm for solving the task. On SO the reaction might be: first figure out your algorithm, then we'll help you implement it.
About What kind of questions should I not ask here? -- this is usually not modified on other sites, and I'm not sure we need it, but here are a few ideas:
Check the MathGroup rules: http://smc.vnet.net/mathgroup.html It gives some ideas about what people tend to ask which might be off topic.
Examples that shouldn't be asked here: questions about pricing/licensing (we're not WRI), bug reports (unless the question is about how to work around a bug)
Other ideas to include (I'll write lots, we'll need to trim the list. Also, these are not for different sections):
How to write formulae (MathJax)
How to post code (what format is preferred considering the REPL interface, and when to post math/images). The main idea here is: it should be very easy to copy the code back to Mathematica. Note: This is an important point, we just had an example of people pasting code as LaTeX for pretty (but uncopyable) formatting.
How to easily upload images (do we need this at all, or keep it as a meta post only? does it make abuse too easy?)
UX has a section about how to ask a good question. I don't personally think we need this (SO doesn't have it either), but it's another idea.
Finally, let me say that I think that a short FAQ is a good FAQ because people are more likely to read it.