Wilcox.test in R I have tried to identify differential expressed genes between two sets of Microarray samples by running wilcox.test for each gene, but the p-values of most of the genes are less than 0.001. How can I find the most significant differences between these two sets?
 A: Presumably you need to identify the groups that are "most different"; differences in p-values aren't necessarily very interesting or informative.
(See for example Gelman and Stern's The Difference Between “Significant” and “Not Significant” is not
Itself Statistically Significant, The American Statistician, November 2006, Vol. 60, No. 4)
So you're left with trying to find where the most important differences lie (actual significance, rather than statistical). 
I assume this is for a Wilcoxon-Mann-Whitney (i.e. two-sample, not paired), but you should clarify. If you're looking at estimating location shift, you then have the two-sample Hodges-Lehmann estimator for the shift - the median of pairwise differences, and there's a corresponding interval for it (which R will produce for you). Among the intervals that exclude 0, you might simply choose the one with the largest estimated difference, but what exactly you might need depends on what you're after.
However, given that you're comparing many such pairs, you might look at using a suitable multiple comparisons procedure for a Kruskal-Wallis test, such as Dunn's test.
A: Since you didn't get any answers yet, let me give you a short answer and maybe you could get a more comprehensive one by someone else.  
If the problem is that you have "too many" p < 0.001, then one thing you could do is to use a correction for multiple comparisons that will correct the p-values (make them higher), you could use p.adjust function in R for that. The simplest one would be Bonferroni correction (dividing p-values by the number of comparisons).
You could also check this slides for more information and ideas what can be done.
