Here are some guidelines I think we should adopt when dealing with hypothetical questions. Michael Edenfield's post on the Sci-Fi and Fantasy blog about this subject is a good read and helped inform my beliefs about how we should handle what-if questions.
Caveat: These are only guidelines. They aren't a formula that will always tell you whether a question should be closed. Use your judgment; if the guidelines are unclear on a question, but your experience suggests that any possible answer will be totally unsubstantiated, go with that.
No cross-universe What-ifs
These are pretty much always opinion-based; they will almost inevitably involve some amount of pure guesswork or unfounded speculation.
Caveat: If there is an official crossover story between two universes, you can ask questions about things that might have happened in that story. For instance, I could ask the question "Does Kyousuke Kousaka think that Ruiko Saten is cute?", because there was in fact an official crossover story between Oreimo and To Aru Kagaku no Railgun. (The answer is yes, by the way.)
Caveat: The burden is always on the question asker to prove that an official crossover exists. If someone shows up asking "Could Naruto beat Luffy? I think they might have crossed over at some point", close the question unless the asker has evidence that they did cross over and might have fought.
What-ifs should be reasonably scoped
This can be tricky to determine if you're not intimately familiar with the series, but basically, any question that would demand an answer summarizing an entire alternate storyline the series could have taken is too broad. As an extreme example, "How would Lelouch's rebellion have gone if he'd never met CC and gotten his Geass?" That asks answerers to rewrite the entire series starting from the very beginning. Educated guesses supported by evidence from the series should be all right, but there is a point where you don't have enough evidence to do that anymore without leaving the realm of reasonable extrapolation.
Makoto's answer has a good set of guidelines to determine if a hypothetical question is reasonable in scope.
What-ifs should obviously relate to the story or the rules of the universe
I like Izkata's comment on the SF&F post that Toshinou-san linked:
Proposed close wording: "Okay, do you have any reason to think this aside from just pulling it out of your ass?"
Of course, we should be more polite than that. But it's reasonable to close a question for being irrelevant or silly or not asked in good faith. We should be able to close things like "What would happen if Motoko Kusanagi ate chili?", because Major Kusanagi eating chili is totally irrelevant to the story or the rules of the universe. (Unless it was strongly hinted at some point that eating chili might corrupt her boot sector and make her slaughter everyone, or something.)
I'm not in love with Death Note lawyer questions, but they relate to the rules of the universe, so they should be allowed. "Does L like chili?" shouldn't be allowed.
"Whatsit-san vs. Who-sama" questions
We get a fair number of these anyway, and I think we've been dealing with them pretty well; the really bad ones I've seen have all been closed. But for completeness, here are the guidelines I'd suggest for them, based on Michael Edenfield's blog:
- Optimally, the characters should have fought at some point. No "Six Degrees of Kevin Bacon here"; if the only way to answer is "Well, XX fought YY who fought ZZ who fought WW, and AA fought BB who fought CC who also fought WW and defeated him, whereas ZZ lost to WW, so going back up the chain, AA wins", it's primarily opinion-based. If you have good reason to think this is the case, vote to close.
- If they haven't fought, use your judgment, but it's probably not looking good for the question. Lean towards closing, but you might ask the OP whether there was an actual scene that made them curious about this. Give extra scrutiny to cases where the characters, for in-universe reasons, never would fight; we might be able to figure out who would win if Sakura without her magic got in a fist fight with Tomoyo, but it would never happen, so the odds are very much against there being any evidence.
- If the characters have never fought, but there are in-universe rules we could use to determine who might win (e.g. "100 Staryus vs. 100 Sandshrew: who wins?"—Staryu, because Ground is weak against Water), the question might be okay, depending on how thoroughly it sets up the scenario and how well the scenario conforms to known canon. But any question that would involve vague arguments about "power levels" or requires answerers to construct elaborate scenarios to answer ("Sandshrew would win because they can throw some desiccants at Staryu to dry up all its water it could buy some desiccants at the Pokemart") is opinion-based
"There's not enough information" or "It's a plot hole" should be valid answers, if the question conforms to the other guidelines
The tough thing about "there's not enough information" or "it's a plot hole" is that you never know if there's some interview or special edition one-shot floating around out there that answers the question, but a good-faith effort should be enough. It's not hard to tell when someone actually put some effort in to cover all the bases before writing the answer vs. when someone just plunked in "Nope, it was never explained, not that I remember".
Answers with official evidence like interviews are best, of course.
Global Caveat: Use your Judgment
We can't cover every possible edge case, and bad questions have a tendency to be really weird. If something looks dodgy to you, go ahead and flag or vote to close. Throw it to the community to judge.
If you vote to close a question and the OP just doesn't seem to understand why, I would encourage you to point them to Meta. Meta should be a place where people can debate individual decisions as well as overarching policy.