Eric Olson has a fascinating paper, 'The Zombies Among Us' (forthcoming in Nous), where he points out that standard constitutional theories of persons imply that our bodies are phenomenal zombies -- physically identical to us but lacking conscious experiences (or indeed any mental properties).
Constitutionalists hold that we are constituted by (but not identical to) the physical matter that makes up our bodies. If we imagine a brain-transplant case, for example, it seems that we go where our brains go, and so we can come apart from our bodies (and likewise from the biological organism that our bodies also constitute). But then we must deny that our materially coincident bodies have mental properties (such as the belief that we go with our brains and not with our bodies), on pain of a fairly radical skepticism (if bodies have all the same beliefs and thoughts as us, what confidence could we have that we are not ourselves such thinking bodies, falsely believing that we go with our brains?).
So, in the ordinary run of things, our bodies are physically identical to us but lack mental properties: they are philosophical zombies.
Not in any sense that refutes physicalism, of course; our brains may still metaphysically suffice for (giving rise to) consciousness, even if we do not then attribute the consciousness to every object that has our brains as parts. (Which makes independent sense, after all: we can speak of a gerrymandered object consisting of my brain + the Eiffel Tower, but we should not hold that this object is itself a thinking thing.)
An interesting consequence of this, which Olson flags, is that physicalists should not identify mental states (or properties) with physical states (or properties). Any token physical state that I am in is shared by my body, after all. So if mental states were identical to token physical states, we would be committed to holding that my body shares my mental states, contra the view expressed above.
Instead, I think, physicalists should agree with dualists that the brain gives rise to (rather than just is) the mind. Their view can remain distinctively physicalistic insofar as they insist that there is nothing metaphysically heavyweight about this "generation" -- the mind comes along "for free", in something like the way that computer hardware gives rise to a running software programme. Your web browser is not identical to any of the circuitry upon which it runs, but nor does it create any deep metaphysical mysteries. (Of course, I think consciousness is different, but I'm playing Devil's advocate for the physicalist here.)
An interesting upshot of this (it seems to me) is that physicalists should be epiphenomenalists too. These "virtual" or abstractly generated mental properties do not push atoms around, and so lack fundamental causal powers (though we can always invoke them when speaking loosely, as in correlative explanations). This isn't a problem, since there's nothing wrong with epiphenomenalism, but insofar as many physicalists believe otherwise, it does put them in a funny position.
[See also: the 'Virtual Mind' diagnosis of why Searle's Chinese Room argument is misleading, for related discussion of how mental properties should be attributed to a different 'level' of entity from that which does the underlying information processing.]