Combination Chemotherapy and Donor Stem Cell Transplant in Treating Patients With Aplastic Anemia or Hematologic Cancer

OBJECTIVES: * Compare the morbidity, mortality, and overall outcome of patients with severe aplastic anemia or hematologic malignancy treated with standard vs novel conditioning regimens followed by allogeneic stem cell transplantation. * Examine the influence of donor histocompatibility on outcome by comparing matched/related, mismatched/related (with or without T-cell depletion), and matched/unrelated transplants with stratification for type of preparative regimen. * Ensure that patients with uncommon diagnoses will be treated in a uniform fashion with the best therapy available. OUTLINE: Patients are stratified according to risk of relapse (standard-risk: acute leukemia in first complete remission, chronic myelogenous leukemia in first chronic phase, lymphoma in sensitive first relapse or second remission, primary or untreated myelodysplastic syndromes, or untreated severe aplastic anemia vs high-risk: all others). Patients are assigned to one of the following conditioning regimens based on diagnosis, risk of relapse, and donor relatedness: * Regimen 1: Patients receive busulfan IV over 2 hours every 6 hours on days -7 to -4 and cyclophosphamide IV over 2 hours on days -3 and -2. * Regimen 2: Patients receive cyclophosphamide IV over 2 hours on days -5 to -2 and anti-thymocyte globulin IV over 4-8 hours on days -5 to -3. * Regimen 3: Patients receive cyclophosphamide IV over 2 hours on days -5 and -4 and total-body irradiation (TBI) twice daily on days -3 to -1. * Regimen 4: Patients receive fludarabine IV over 30 minutes on days -6 to -2 and melphalan IV over 1 hour on days -3 and -2. * Regimen 5: Patients receive etoposide IV over 26 hours beginning on day -5, cyclophosphamide IV over 2 hours on day -4, and TBI twice daily on days -3 to -1. * Regimen 6: Patients receive cyclophosphamide IV over 24 hours, carboplatin IV over 24 hours, and thiotepa IV over 24 hours on days -7 to -4. * Regimen 7: Patients receive fludarabine IV over 30 minutes on days -5 to -1 and anti-thymocyte globulin IV over 4-8 hours on days -5 to -2. * Regimen 8: Patients receive cyclophosphamide IV over 2 hours on days -5 and -4, TBI twice daily on days -3 to -1, and anti-thymocyte globulin IV over 4-8 hours on days -3 to -1. * Regimen 9: Patients receive busulfan IV over 2 hours every 6 hours and anti-thymocyte globulin IV over 4-8 hours on days -7 to -4 and cyclophosphamide IV over 2 hours on days -3 and -2. All patients then receive donor stem cell infusions on day 0. Some patients may undergo involved-field radiotherapy 4-8 weeks after transplant. Patients will be taken off study after a minimum of 4 years of follow up. PROJECTED ACCRUAL: At least 405 patients will be accrued for this study within 5 years.