Reduced Intensity Total Body Irradiation + Thymoglobulin Followed by Allogeneic PBSCT

Inclusion Criteria: * Patients with hematological malignancies for which allogeneic stem cell transplantation indicated including non-Hodgkin lymphoma (NHL), multiple myeloma (MM), acute myeloid leukemia (AML), Hodgkin lymphoma (HD), chronic lymphocytic leukemia (CLL), chronic myelogenous leukemia (CML), and myelodysplastic syndrome (MDS) * Patients with HLA compatible related or unrelated stem cell donor, willing and able to serve as an allogenic HSC donor. Unrelated donors have to be matched at HLA-A, B, C and DRB1 loci. A single locus mismatch will be tolerated in the event a more closely matched donor is not available. * Patients age \>/=40 to \</=70 with an ECOG performance status \< 2 * Patients between 18 and 40 years of age will be eligible only if they have co-morbidities precluding conventional allogeneic transplantation with full intensity myeloablative conditioning * Adequate cardiac, pulmonary, renal and hepatic function for transplant * Negative serology for HIV * Negative serum pregnancy test * Patients who have received therapeutic radiation to a localized field will be eligible, provided critical structure tolerance doses have not been exceeded * Patients who have had prior myeloablative autologous transplant will be eligible Exclusion Criteria: * Evidence of uncontrolled viral, fungal, bacterial infection * Evidence of active meningeal or CNS disease * Prior therapy with rabbit ATG, prior treatment with equine ATG is allowed if more than 3 months ago * Breast feeding mothers are excluded