in general you should first check the normality of your sample. To do that you can use either the Kolmogorov-Smirnov test of the Shapiro-Wilk test. The you decide if you can use parametric methods (such as T-test, ANOVA) or non-parametric (such as Mann-Whitney U, Kruskal-Wallis etc.). This applies if your variables are interval or ordinal. Of course if you have nominal variables you always use non-parametric methods such as Chi-Square tests.