A good charop question is either very specific or very general. If you fall in between you've entered the no mans land of gimmie the codez.
There are 3 types of char-op questions that fall into the "good" category in my mind:
I'm 90% complete and I need help making the final selection or two. These kinds of questions are generally answerable because they have a pretty finite set of answers and there are usually a pretty obvious set of "Best" answers. Unfortunately the downsides to these is that they are often too localized, but they help a user with a specific problem that others may encounter so maybe not. (Examples 1 2 3(meh, but ok))
I need some general advice on direction for a build. These kinds of questions, while significantly more broad are the magnet for low quality, the key here is for the questioner to give some requirements that can lead to some general character advice. If they need a full handhold through building a character they should probably be seeking a message board or at least our chat rooms. But if they have some ideas and need a starting point we can help. This has the advantage of being useful if someone comes along with similar requirements. (Examples 1 2 3)
The last kind of question that I see as useful is the challenge question. These are the most borderline Op questions IMO, but they can also be the most fun. (Examples 1 2 3)
Basically if the question is specific enough with requirements for the first and third, or has enough background that we can help with broader class/race/build help in the 2nd (if someone want's to provide a full character workup that's great, but that shouldn't be the expected answer from question type 2) then we can continue to take these question and they can continue to be more or less constructive.
The common thread here is that the asker provides answerable requirements. As Brian says below if a thread does not have answerable reqs then we should be voting to close until they provide them.
My examples mostly come from 4e questions that I'm familiar with, anyone with edit powers feel free to add good or better examples of each of the 3 question types. I've made this CW so the bar to edit is lower.