I've always found SE's strength to be its ability to answer specific, specialized, and even obscure questions at a very high level of both eloquence and expertise. So the questions I find most representative are the ones that are:
- specific and well-focused,
- dealing with a particular, perhaps unusual niche of the craft, and
- difficult to answer easily with Google or "see what works for you" answers.
As such, here's my list.
I'm sure there are more, but these are enough to demonstrate what I'm most looking for.
Each of these copes with a specific tough problem that even an experienced pro could have trouble with; in all of them, a solution is not obvious to somebody who isn't familiar with that particular subject. We do great with lots of other types of questions as well, but it's these where I think that as a Stack Exchange site, we can stand out the best - these are great issues and questions that would be very tough to get answers for anywhere else.
Another question I'd like to see more of is Does my story structure for an ensemble zombie story sound effective? . I'm generally not a huge fan of critique questions, because I find it hard to critique effectively based on very small samples, and because they're difficult to focus well. But a request to critique a proposed structure works really well, can get great responses, and (again) this is a type of question that would have trouble getting a good answer elsewhere.
NOTE: The other thing I'd really like to see is more questions from segments other than fiction writers. Technical writers, biographers, reporters, editors, proofreaders, critics, copywriters... We've got plenty of room for 'em, but so far, we just aren't seeing much of any of 'em. That's the other area I see for potential expansion that'd be really great.