I had the same questions and made some research.
I came across some texts that seem to offer solutions but I ahve to admit that I did not seriously apply them until now.
- Feller, A., Holmes, C.C., 2009. Beyond toplines: Heterogeneous treatment effects in random-ized experiments.
- Leys, C., Schumann, S., 2010. A nonparametric method to analyze interactions: The adjusted rank transform test. Journal of Experimental Social Psychology 46 (4), 684–688.
- Sawilowsky, S.S., 1990. Nonparametric tests of interaction in experimental design. Review of Educational Research 60 (1), 91–126.
At least for 1. it seems that you rely on a sufficiently large sample size. They analyze a dataset which has between 38,00 and 190,000 observations per treatment. If you are working with experimental data from a laboratory and are from the behavioral field, this is probably not very helpful. However, I find their analysis of interaction effects, especially their graphical interpretation, very vivid and intuitive.
The 2. text discusses one of the approaches that are discussed in 3. It has been a while since I read the latter paper, but if I remember correctly, the author presents some approaches to analyze interactions non-parametrically in a practical way. As probabilityislogic said, people often criticize that non-parametric tests of interactions lack power. However, Sawilowsky (1990) states that "The review shows that these new techniques are robust, powerful, versatile, and easy to compute." On the other hand, the text is quite old ;)
Other approaches, of which I only know the name, are Finite Mixture Models and Latent Class Regression Models. One of the two is a special form of the other, but I do not remember which one.
Hope this helps.