Allogeneic Stem Cell Transplantation Following Chemotherapy in Patients With Hemoglobinopathies

* In order to undergo transplant procedure, patients will be admitted to the hospital for approximately 10-14 days. * To prepare patient's bone marrow to accept donor stem cells, they will receive fludarabine and busulfex. Fludarabine will be given intravenously once daily for 4 days. Busulfex will be given once daily for the same 4 days. * One day before patients receive busulfex and fludarabine, they will also be given alemtuzumab intravenously once daily for 5 days. * Three days after the end of chemotherapy, patients will receive the infusion of donor stem cells. * If patients have thalassemia, they will receive subcutaneous injections of filgrastim starting on day one after the donor stem cell transfusion and will continue receiving filgrastim every day until it appears that the donor stem cells have been accepted. If the patient has sickle cell disease, filgrastim will not be given, * Additional drugs will be given to help prevent infection (i.e. antibiotics). * After stem cell infusion patients will be examined and have blood tests weekly for 1 month. Bone marrow biopsies, and blood work will also be performed 1 month, 3 months, 6 months and 1 year after stem cell infusion. * Patients will be on the study for about 12 months. After study is completed progress will be monitored on an annual basis.