Richard has been posting on personal identity at Philosophy, et cetera. I left a comment that, in retrospect, should be a post in itself. So, here it is, with clarifications. It suffers a bit from the obscurity that always follows on my commenting; but I hope it's clear enough.
I'm not convinced Parfit avoids the need for a 'further fact' [beyond psychological and physical continuity in personal identity]. That is, he needs not just continuity, but continuity relevant to preserving personal identity. Any change the body undergoes, for instance, would exhibit continuity, simply because that's the way physical change works. (Psychological change is trickier, but we can presume it the same for our purposes; the point would be moot for most physicalists anyway, given the issue with physical change.) Parfit himself occasionally talks of "full continuity", and I am not convinced that that 'full' isn't in fact dragging in a 'further fact', i.e., something that must be preserved through the continuity.
And I think this actually gives away the store to the ego theorist, who doesn't have to hold that the ego is a 'pure ego' unmodified by anything psychological and physical; she just has to posit a unifying subject to which the relevant psychological and physical acts are referred. In other words, the old idea that to actually have continuity through change, something must remain through it, a subject of the change, which is a precondition for saying "There is real continuity here". And, whatever its nature (or even if it changes over time itself) when we are talking about ordinary personal identity, we just call this subject of change the ego, or person, or what have you, because that's the type of change we're looking at. (I think, in fact, that this is precisely what has traditionally been intended by ego theories, and it is what Parfit misses about them.) What happens in the typical philosophy of mind Crazy Sci-Fi Cases is irrelevant unless we have a handle on whether there is a subject of change in those cases. And the reason there is sometimes no answer to whether we will persist through a change proposed by these cases is that the cases are not clear and precise enough about what is going on for us to get a handle on whether there is a subject of change.
I think the reason, though, that personal identity is supposed to be deeply significant is precisely Locke's reason: whatever the metaphysical reality, we simply can't do without personal identity forensically: i.e., morally and legally. We need it to have a viable theory of responsibility. And this also requires that we have more of a handle on what is actually going on in the change than the Crazy Cases give us.
So in other words, (1) identifying something as a relevant continuity seems to require a 'further fact' itself; (2) the Crazy Cases aren't clear enough to tell us anything metaphysically; (3) the Crazy Cases aren't clear enough to tell us anything forensically; (4) it is utterly unclear why we are using them at all (I tend to follow Kathleen Wilkes's line in Real Persons on this whole issue). But it's been ages since I've read Parfit, so he might have some reasonable response to this that I've forgotten.