I have a simple, pragmatic approach, simply for the purpose of being able to generate a ratio, which is the following: add a small number to all values. e.g. for RNA Seq data I might add 0.01 to all values. Thus you can then calculate a ratio such that large values are virtually unaffected, and small values are also not affected very much. If you then plot the data in log2 space (i.e. using an MA plot where M is log2(value1/value2) on the y-axis, and A is log2(sqrt(value1*value2)) you can evaluate ratios, and the magnitude of the numbers that make up those ratios, and weight things accordingly.
I disagree that fold change is not very informative, and that null values for one of the conditions should be discarded or ignored. As a biologist and an experimentalist, I can get a lot of insight if a given gene has no counts in one sample, and many counts in another, and indeed it's what I might expect from a gene differentially regulated under a given set of conditions. Using the MA plot, one can also avoid the folly of large ratios that come from small numbers (i.e. I can distinguish a ratio composed of one reasonable component and one small component - which is interesting, from a ratio that comes from two small but different components - where a large ratio may result but neither component would be a trustworthy measurement).
Of course, if you have p-values, then those are what should be used for evaluation. Also, the trick above is simply pragmatic so the ratios can be evaluated for ideas, and should be explicitly noted as such. I leave the individual measurements untouched, so that once an interesting set of ratios is selected, the genes can be evaluate for those that have zero counts.
This approach is likely to make a statistician groan in pain, but not more loudly than the experimentalist being told that he can't evaluate the data because one of the measurements was zero. (as an analogy, if the scientific question is: am I wealthy? And I'm trying to detect any fold change between myself and a person standing next to me, if I have $100 in my pocket and they have zero, it's more useful to add a penny to both our pockets and answer the question, than to be told the question can't be evaluated because their pockets are empty).