While improved medical care has allowed many people with these diseases to live longer, the only way to truly cure the diseases is by means of a stem cell transplant from a donor who does not have the disease. A stem cell transplant will replace sick cells with new healthy donor cells. Stem cells grow into different types of blood cells that people need, including red blood cells, white blood cells, and platelets. In a stem cell transplant, the patients own stem cells would be killed by chemotherapy drug and then replaced by stem cells from the donor. Stem cells can be collected from the bone marrow, peripheral blood or umbilical cords. In this study, umbilical cords will be the source of the stem cells.