The zombie scenario just assumes, without argument, that a fully-specified physical world contains no consciousness. The amoralist case just assumes, without argument, that full knowledge of morality will not give sufficient motivation to act. The Frankfurt-style examples just assume, without argument, that being under the control of a counterfactual demon is still a case of genuinely free choice in action. And the direction of fit metaphor just assumes, without argument, that these two directions of fit must both exist. In other words, the cases are structured in such a way as to appeal solely to intuitions favourable to one side of a philosophical dispute, bypassing the inconvenient "giving an argument" stage completely.
All very true, I grant, but there's nothing wrong with this. To see why, suppose I were to claim that 'bachelor' is defined to mean 'unmarried man'. You might respond with putative counterexamples, e.g. pointing out that the Pope is an unmarried man, but (intuitively) not a bachelor. It would be odd for me to complain, "You're just assuming, without argument, that the Pope is not a bachelor!" True, you say, but I'm missing the point. You merely wanted to draw my attention to a possibility that I may have neglected. Do I really deny that the Pope is no bachelor, you ask? If so, we must look elsewhere to resolve our disagreement. But it was not unreasonable for you to offer the suggestion that you did: you had every reason to expect that it might inform my view, even though I did not antecedently agree with your conclusion that there could be unmarried men who aren't bachelors.
Compare Stalnaker's wonderful insight:
With riddles and puzzles as well as with many more serious intellectual problems, often all one needs to see that a certain solution is correct is to think of it--to see it as one of the possibilities.
Sometimes a vivid illustration is all we need to advance our understanding, and so make philosophical progress.
With this in mind, I think it helps to understand 'begging the question' in dialogical (rather than purely logical) terms. Every valid argument contains its conclusion in its premises, after all. So that alone can't be grounds for complaint -- there's nothing wrong with drawing out implicit commitments which one hadn't previously appreciated. Rather, what's problematic is if an argument is not going to be rationally persuasive to anyone who doesn't already accept the conclusion. Fruitful debate merely calls for arguments that are dialectically effective for logically non-omniscient agents such as ourselves. Some arguments aren't going to help advance the dialectic at all, so it's those which I would call 'question begging'.
The thought experiments Adam discusses aren't like that though. Many people are persuaded upon learning of zombies and Frankfurt cases. These thought experiments make vivid to us certain conceptual interrelations which we had not fully appreciated beforehand. That said, further argument will be required if someone sincerely disputes the proffered description of the scenario in question (as Adam suggests). But that merely shows that these thought experiments are not guaranteed to be dialectically effective. That's fine; there's plenty of space between 'knock down' and 'mistaken' for these arguments to occupy.