R (I think it was R) introduced a practice in which multiple asterisk characters are used to indicate different significance levels for tests. [Correction: Bill Idsardi points out some prior art that probably predates the R convention. I have no idea what S or S-Plus did, nor what R was like before 2006 or so. But certainly R has helped popularize it.] For instance, in R statistical summaries, * denotes a p-value such that .01 < p < .05, ** denotes a p-value such that .001 < p < .01, and *** denotes a p-value < .001. This type of reporting increasingly can be found in papers also, but there are good reasons not to copy R’s bad behavior.
In null hypothesis testing, the mere size of the p-value itself has no meaning. All that matters is whether p is greater than or less than the α-level. Depending on space, we may report the exact value of p for a test (often rounded to two digits and “< .01″ used for abbreviatory purposes, since you don’t want to round down here), but we need not. And it simply does not matter at all how small p is when it’s less than the α-level. There is no notion of “more significant” or “less significant”.
R also uses the period character ‘.’ is used to indicate a p-value between .05 and .1. Of course, I have never read a single study using an α-level greater than .05 (I suppose this would simply make the possibility of Type I error too high), so I’m not sure what the point is.
My suggestion here is simple. If you want, use ‘*’ to indicate a significant (p < α) result, and then in the caption write something like “*: p < .05″ (assuming that your α-level is .05). Do not use additional asterisks.