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I don't know about others, but when I answer a question in the comments it's usually because either 1) I secretly feel that the question is not appropriate for MO, but it's borderline enough that I want the OP to have an answer anyway, or 2) I'm not confident in the answer and I want someone to tell me I'm wrong. If answers are being given for the second reason then they probably shouldn't be copied as actual answers. Maybe this is a case-by-case thing (or maybe other people don't do 2)).
In the case that the user is still active, we should copy the comments over to an answer, and make the answer community wiki if you feel bad about it.
In the case that the user has not been back in the past n months, add the answer as above and vote to close, for n to be decided by the community.
Qiaochu's description of why questions get answered in the comments sounds right to me. Basically, I think that if a question has been answered in the comments and is now dormant, you should do whatever you think is best for future generations. Imagine that somebody has come to the question through a google search, decide what would be optimal for them to see, and move the thread in that direction (which may mean doing nothing).
If it looks like a question was answered in the comments because the question wasn't appropriate for MO, it's still not appropriate for MO, so you should vote to close for whatever reason fits the question. However, I don't think it's right to vote to close a question simply because it has been answered.
If it looks like the person answering wasn't very confident in her answer (or just wanted to get a terse answer out), but you think she should post it as an answer, I think you should either post it as a CW answer or leave a comment to the effect of "@username: I think you should post that as an answer." (this will be more effective when we finally get replies to comments merged from SO). The advantage of CWing the answer is that people with <2000 rep can then edit it to make it better if it was incomplete in some way.
I've also been mulling over the question Pete mentioned. I'm not completely sure that posting Pete's comment as an answer was the right thing to do, but I don't regret it. For questions that might be homework, I feel like it's reasonable to post an actual answer which consists of a reference. This gets around the problem of unanswered-but-actually-answered questions. If it wasn't homework, this is exactly what the asker was looking for, and if it was homework, the asker still has to work through the reference. The main reasons for discouraging homework questions are (a) we want to get the right audience (research mathematicians, not calculus students), and (b) it's annoying when somebody asks you to do his work for him without having put any effort in. Somehow the question Pete mentioned didn't feel to me like somebody gaming MO to do their homework, and it was an appropriate subject matter, so it didn't trigger my "inappropriate question detector".
3) another possibility is that there is a very simple answer/counterexample and it's unclear whether the author meant to ask the question as stated or left out a hypothesis. In such cases it's clearly better to address this in the comments to give the author a chance to fix the question.
If the question is unclear, I would vote to close and leave a comment asking the OP to clarify (and perhaps link to http://mathoverflow.net/howtoask). Once the question has been sharpened, vote to reopen. It's really frustrating when any answer to the question has to start off with a guess about what the question actually is. Typically, the OP realizes that something is wrong after a couple of answers have been posted, then edits the question so the answers look totally bogus. Closing the question until it's cleaned up prevents this sort of thing from happening.
I would say that if you wouldn't vote to close the question, absolutely you should post the answer. part of the point of MO is to have a canonical place on the internet to stick a question and its answer in a way that makes it immediately apparent what the answer is. I think the community norm which makes us feel as though we are "stealing" an answer if we weren't the originator of it is a counterproductive one. If you feel uncomfortable "claiming" the answer, you can make it community wiki, but it is a positively thing for later users of the site to have the answer in the answer box, hopefully voted up a few times.
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