Allogeneic Transplantation Using Total Lymphoid Irradiation (TLI) and Anti-Thymocyte Globulin (ATG) for Older Patients With Hematologic Malignancies

INCLUSION CRITERIA: * Any patient with one of the following hematolymphoid malignancies or syndromes in whom allogeneic hematopoietic stem cell transplant (HST) is warranted. Specific disease categories include: * Indolent advanced stage non-Hodgkin lymphomas * Mantle cell lymphoma * Chronic lymphocytic leukemia * Hodgkin disease (Hodgkin's lymphoma) * Acute leukemias in complete remission * Aplastic anemia * Paroxysmal nocturnal hemoglobinuria * Myelodysplastic or myeloproliferative syndromes. * Other selected malignancies/disorders may also be considered but must be approved by the transplant team and the Principal Investigator. * Age \> 50 years, or if \< 50 years of age, considered to be at high risk for regimen-related toxicity associated with conventional myeloablative transplants due to pre-existing medical conditions or prior therapy. * A fully human leukocyte antigen (HLA)-identical sibling or matched unrelated donor is available. Potential participants with one antigen mismatched donors can be considered but only after discussion with the transplant team and the Principal Investigator. * Participant must be competent to give consent. EXCLUSION CRITERIA: * Progressive hematolymphoid malignancies despite conventional therapies, or acute leukemias not in complete remission. * Uncontrolled central nervous system (CNS) involvement with disease * Fertile men or women unwilling to use contraceptive techniques during and for 12 months following treatment * Pregnant * Cardiac ejection fraction \< 30% * Uncontrolled cardiac failure * Pulmonary diffusing capacity (DLCO) \< 40% predicted * Elevation of bilirubin to \> 3 mg/dL * Transaminases \> 4 x the upper limit of normal * Creatinine clearance \< 50 cc/min (24-hour urine collection) * Karnofsky performance score \< 60% * Poorly controlled hypertension on multiple antihypertensives * Documented fungal disease that is progressive despite treatment * HIV-positive. Other viral infections, ie, Hepatitis B- and C- positive, evaluated on a case-by-case basis * Psychiatric disorders or psychosocial problems which in the opinion of the primary physician or Principal Investigator would place the patient at unacceptable risk from this regimen.