Non-parametric tests make fewer assumptions about the distribution of data compared to parametric tests. They can be used as alternatives when the assumptions of parametric tests like the t-test, ANOVA, and other tests are violated. Some common non-parametric tests include the Mann-Whitney U test and Wilcoxon signed-rank test for comparing two independent and paired samples respectively, and the Kruskal-Wallis H test for comparing more than two independent samples. These tests convert original data to ranks before performing the statistical analysis to avoid distributional assumptions.