Q:

What should be the policy on "open problems" on MO?

The subject of this discussion are questions on "open problems" on MO.
There is an existing policy on "open problems" reproduced from the (old) FAQs, which involves an open-problem tag.
The motivation for starting this discussion are comments on said post, various users have expressed concerns related to the existing policy or at least the way it is described. This description is now also somewhat more visible as it essentially became (and naturally so) the description of the open-problem tag. 
Answers could take the form of approving what we currently have, basically approving but suggesting minor modifications, suggesting major changes, and so on. 
This concerns primarily the description of the policy, but discussion on how things are or should be handled in practise are also welcome.

A:

I thought the policy was the following, and I continue to think that it should be the policy:

Questions asking about famous open problems are typically closed
Questions that turn out to be less-famous open problems, but still well-known to experts, are answered by giving a reference to somewhere that the openness of the problem is discussed.
Questions which turn out to be hard but are not previously well-known are on-topic and encouraged.

So basically "I like this problem and no one I've asked can answer it" is great but "Every expert in subfield X has thought about this problem and gotten stuck" is bad.

A:

I think that we should explicitly welcome open questions. 
I mean this, first, in a narrow sense. Namely, every mathematician hopes that the questions on which they are currently working---whether for their dissertation or a later project----is an open question. These open questions come in all types, some interesting, some difficult. Let us welcome them here and give them our attention and consideration. I suspect that with the talented people we have here on MO, many of these questions will find an answer. This is a sense in which I think that nearly everyone already agrees on the matter.
But second, in a wider sense, I think that it would actually be good for the site for us to encourage people to ask open questions of all sorts, including very prominent ones. Surely there is a continuum of open questions ranging from very easy ones up to the more normal MO questions and on up to the famous open questions. There already are some very interesting open questions on MO, such as the question on polynomial bijections from $\mathbb{Q}\times\mathbb{Q}\to\mathbb{Q}$ and many others, which I think of as highlights of the site, even though they are open. Let's build a collection of the best questions in mathematics! As answers, we can post information about resources, history, partial solutions, related problems.
I would expect that many of the more famous open questions could become some of the highest-voted questions on the site, a situation that would address the worry some have had about other softer questions currently occupying that role. 
Imagine that the top-voted questions on MathOverflow were all the most popular open questions in mathematics! That would be great.

A:

Second draft (please see my other answer for context):
What about open problems?
It depends on what is meant by an open problem: here, we mean a problem which is well-known to be unsolved and very hard. Questions for which you simply do not know the answer are not the issue, as those are the norm on MathOverflow.
On the one hand, a question which simply states a famous open problem will often not be well received. If you mainly want to record some open problem, this site is not the appropriate place: you may do so at the Open Problem Garden, for example.
On the other hand, questions that touch upon a well-known open problem are certainly welcome, as long as they follow the general guidelines for asking on MathOverflow [[comment: perhaps placing a link here to the guidelines would be a good idea]]. Nevertheless, when asking about an open problem, you should mention that it is known to be unsolved. In this case, please use the open-problem tag, in addition to other appropriate tags.
Most importantly, please remember that MathOverflow is a question and answer site: the prototypical question is posed under the assumption that some other user will be able to answer it. This principle also applies to questions about open problems. For example, the community will usually welcome inquiries on partial progress, results in special cases, etc.
What if my question turns out to be a well-known open problem?
If you ask a question which is widely known to be unsolved, someone will typically point that out and provide references to the relevant literature. In most such cases, this is the best answer one can expect. At this time, you can add the open-problem tag to your question. If you then have more detailed follow-up questions, feel free to ask them in new posts.

