Total Body Irradiation +/- Total Lymphoid Irradiation & Anti-Thymocyte Globulin in Non-myeloablative Hematopoietic Cell Transplantation

INCLUSION CRITERIA * Has a human leukocyte antigen (HLA)-matched or single allele mismatched adult sibling donor or unrelated donor. * Acute myeloid leukemia (AML); myelodysplastic syndrome (MDS); myeloproliferative disease syndrome (MPD)\]; chronic lymphocytic leukemia (CLL); B- or T-cell non Hodgkin lymphoma (NHL); Hodgkin lymphoma (HL); or chronic myelomonocytic leukemia (CMML), suitable for treatment with allogeneic transplant after TLI and ATG reduced intensity conditioning. * Considered at high-risk for regimen-related toxicity from fully-ablative transplant conditioning (therefore reduced-intensity conditioning is recommended). * Ability to understand and the willingness to sign a written informed consent document. Patients must have signed informed consent to participate in the trial. EXCLUSION CRITERIA * Uncontrolled bacterial, viral or fungal infection defined as currently taking medication and progression of clinical symptoms. * Progressive hemato lymphoid malignancy despite conventional therapy. * Chronic myelogenous leukemia (CML). * Active CNS involvement of the underlying malignancy. * HIV positive * Pregnant or lactating * Prior malignancy (EXCEPTION: diagnosed \> 5 years ago without evidence of disease, OR treated ≤ 5 years ago but have a greater than 50% chance of life expectancy of ≥ 5 years for that malignancy). * Have a psychiatric disorder(s) or psychosocial circumstance(s) which in the opinion of the primary physician would place the patient at an unacceptable risk from transplant. * Left ventricular ejection fraction (LEVF) \< 30%, or uncontrolled cardiac failure * Diffusing capacity of lung for carbon monoxide (DLCO) \< 40% predicted * Total bilirubin \> 3 mg/dL * Serum glutamic oxaloacetic transaminase (SGOT) or serum glutamic-pyruvic transaminase (SGPT) \> 4 x upper limit of normal (ULN) * Creatinine \> 2 mg/dL and an estimated creatinine clearance \< 40 mL/min * Poorly-controlled hypertension despite multiple antihypertensive medications * Karnofsky Performance Status (KPS) \< 60%