I can't find an appropriate definition of what the homework tag should cover. Is it homework if it is not to be handed in? Is it homework if it is an exercise from a book during self-study? Is it homework if it is a question which has come up while preparing for a test?
I'll bite. It's homework if
You're a student, and
Your teacher told you to do it, and
You're expected to do it on your own, or report any help you got on it.
There should be a situation like this (although MSE seems unable to make it work...):
You have a problem you want to solve yourself, you state it here and show what you did so far and where you got stuck. You want us here to provide you merely with a small hint to help you proceed. You do not want us here to write the complete solution within 10 minutes.
That is a "homework" or "homework-type" question.
The burden is on our users here. When they see the "homework" tag they should restrain themselves and not post a complete solution. That is the part that doesn't work here. Even if 99 percent of us do it, there is often that one guy who goes ahead with the solution.
Without meaning to take anything away from any other comments or answers, I would (reiterate that) an exogenously-assigned homework, with a due date, with "judgement" coming due, is essentially infinitely different from any sort of self-assigned task. I had always presumed that "homework" meant that the questioner had limited idea of the context of the question, also, and, in any case, might have limited motivation to understand any larger context, but "needed" to come up with an answer ... e.g., to avoid a bad grade. That is, ... apart from any apparent intellectual/scientific/aesthetic motivations.
I have no serious objection to motivation-by-coursework, but, yes, cliche'd questions thus arising have a different, and somewhat delicate, status, in contrast to questions arising outside of such an environment.
Semantics aside, homework is a problem assigned to you by your course instructor and the due date hasn't passed yet. If the due date has already passed then it's no longer a homework.