The SPSS Exact Tests module offers exact or monte carlo significances (p values) for nonparametric tests, including those in the NPAR TESTS procedure and almost all measures available in the CROSSTABS procedure. General ANOVA models are not included, only one-way between-subjects models on ranks (Kruskal-Wallis) and one-way repeated-measures on ranks (Friedman test). It is possible to perform these tests "manually" in SPSS by randomly assigning cases to groups or cells, running the model based on each of the pseudo-assignments and capturing the results via the OMS (Output Management System) command in order to compare the observed result with the empirical distribution of results, but this would require nontrivial custom programming
For R, you can read lecture at http://faculty.washington.edu/kenrice/sisg/SISG-08-06.pdf.