Any other non-parametric alternative to Kruskal-Wallis? It looks like Kruskal-Wallis is the standard nonparametric test for more than two groups. The problem is that it does not tell which groups are different, except that whether there exists significant difference among the groups.
Is there another nonparametric test for more than two groups? Or better, is there one that would tell you which groups are different?
 A: You can still run the Kruskal-Wallis, all you need to do is run subsequent pair-wise tests comparing each group to the other groups.
After running a Kruskal-Wallis test and determining that there is a significant difference, you could run additional post hoc tests, for example a Dunn's test, to compare each individual group and determine which are significantly different from each other.
For a reference to the rationale for a Dunn`s test vs. Wilcoxon Rank-sum:
Post-hoc tests after Kruskal-Wallis: Dunn's test or Bonferroni corrected Mann-Whitney tests?
For the original paper describing the test:
Dunn OJ. Multiple comparisons using rank sums. Technometrics 1964; 6(3):241-52.
http://dx.doi.org/10.1080/00401706.1964.10490181
A: The generalization of the Kruskal-Wallis test is the proportional odds ordinal logistic model.  Such a model can provide the multiple degree of freedom overall test as you get with K-W but also can provide general contrasts (on the log odds ratio scale) including pairwise comparisons.
