The current version of SPSS has several of the common non-parametric tests which include but not necessarily limited to the following:
The Kruskal Wallis test (commonly substituted for the ANOVA) ;
The Wilcoxon signed rank sum test(commonly substituted for the parametric Student's T-Test)
The Friedman test (frequently substituted for the One Way ANOVA with Repeated Measures)
Mann-Whitney U Test (commonly substituted for the independent samples T-test)
Chi square test for independence & Chi square test for goodness of fit
Kappa measure of agreement
I would suggest using the SPSS Survival Manual by Julie Pallant for discussing the procedures on how to run specific non-parametric tests if you're not familiar with how to do so; alternatively the SPSS website has a help file on running non-parametric tests which can be found here: