It is a commonplace that correlation does not imply causality, however eyebrow-wagglingly suggestive it may be of causal hypotheses. It is less commonly noted that causality does not imply correlation either. It is quite possible for two variables to have zero correlation, and yet for one of them to be completely determined by the other.
There is a really interesting discussion/debate about Pearl's and Rubin's approaches to causal inference going on at Andrew Gelman's Blog. Part One. Part two. Part three.
Pearl is contributing in the comments.
Thanks! This stuff looks interesting. I would appreciate a short summary; could write it myself if I have the time.