Some common toxicity tests include the Ames test, LD50 test, Micronucleus test, and Comet assay. The Ames test assesses the mutagenic potential of a substance, the LD50 test determines the lethal dose for 50% of a test population, the Micronucleus test detects chromosomal damage, and the Comet assay evaluates DNA damage in individual cells.