Went for "conceivable but not metaphysically possible".
It seems pretty clear to me that we can and do "conceive" of zombies, or of other puzzles like inverted spectra (you see red while I see green, but we're both looking at the same tree, and both call the tree "green"). However, this is because of a mental trick in the way we conceive mental states.
Basically, for normally-sighted people, it seems that when we imagine a physical object (like a tree), we imagine it from an external perspective. We induce in ourselves a mental state similar to the one we would get from looking at the object concerned (the tree). However, when we imagine a mental state itself (such as an experience of green), we do so sympathetically, or from an internal perspective, by inducing in ourselves the same or a similar mental state.
So this allows us to "mix and match" brain states and mental states. For instance, I can imagine your brain while you are looking at a tree (I have a mental picture of grey matter with lots of neurons firing) while at the same time imagining the mental state of experiencing red. No problem at all... it seems perfectly conceivable that these could happen together; instant inverted spectrum. Or I can imagine the same brain state (same grey matter, same firings) while not imagining a mental state at all (it's all neurons firing in complicated chains, but no-one's at home)... again seems perfectly conceivable that these could happen together; instant p-zombie.
But it's all just a dumb quirk of imagination. Because of the different imaginative techniques, we fool ourselves into conceiving apparent possibilities that aren't really possible after all. One way to debug the imagination is to ask ourselves this: "Suppose I were forced to imagine a mental state from the external perspective, the same way I imagine a tree. What would that look like?" And the short answer is "Well, without scientific evidence, I really don't have a clue. I have no intuition whatseover about what a mental state really looks like from the outside. Up to now, I've always imagined one from the inside. From the outside perspective, it might just as well be a brain state as a soul state or an ectoplasm state. So I'd best follow the science wherever it's pointing".
Despite being (IMO) a philosophy blog, many Less Wrongers tend to disparage mainstream philosophy and emphasize the divergence between our beliefs and theirs. But, how different are we really? My intention with this post is to quantify this difference.
The questions I will post as comments to this article are from the 2009 PhilPapers Survey. If you answer "other" on any of the questions, then please reply to that comment in order to elaborate your answer. Later, I'll post another article comparing the answers I obtain from Less Wrongers with those given by the professional philosophers. This should give us some indication about the differences in belief between Less Wrong and mainstream philosophy.
Glossary
analytic-synthetic distinction, A-theory and B-theory, atheism, compatibilism, consequentialism, contextualism, correspondence theory of truth, deontology, egalitarianism, empiricism, Humeanism, libertarianism, mental content externalism, moral realism, moral motivation internalism and externalism, naturalism, nominalism, Newcomb's problem, physicalism, Platonism, rationalism, relativism, scientific realism, trolley problem, theism, virtue ethics
Note
Thanks pragmatist, for attaching short (mostly accurate) descriptions of the philosophical positions under the poll comments.
Post Script
The polls stopped rendering correctly after the migration to LW 2.0, but the raw data can be found in this repo.