What You Need to Know About 5 Most Common Genetic DisordersDown Syndrome. Typically, the nucleus of an individual cell contains 23 pairs of chromosomes, but Down syndrome occurs when the 21st chromosome is copied an extra time in all or some cells. … Thalassemia. … Cystic Fibrosis. … Tay-Sachs disease. … Sickle Cell Anemia. … Learn More. … Recommended. … Sources.