Paraphrasing Jeff Martin (from an email conversation):
I've always advised to round all of these to "<0.001". This is because many of the techniques to derive p values are approximate and stating the exact numerical value of very small p values gives a false sense of accuracy.
This is unless one is in the realm of multiple comparisons and needs to show the exact nature of the very small value. In these instances, one should be sure that one is using exact (rather than approximate) statistical techniques.