This is a pilot clinical trial of hematopoietic stem cell transplantation for patients with the diagnosis of a genetic disease of blood cells that do not have an HLA-matched sibling donor. The stem cells will be derived from a 1) matched unrelated donor (MUD) or 2) unrelated umbilical cord blood (UCB). Patients will receive a novel conditioning regimen with Busulfan, Cytoxan and Fludarabine (Bu/Cy/Flu) and either Alemtuzumab (Campath 1H) for recipients of a MUD or rabbit Antithymocyte Globulin (rATG) for recipients of unrelated UCB prior to hematopoietic stem cell transplant (HSCT).