The central hypothesis of this study is that use of a less toxic chemotherapy preparative regimen for allogeneic hematopoietic stem cell transplantation in combination with T cell depletion with alemtuzumab for patients with high risk hematologic malignancies will allow effective control of disease and improved disease free and overall survival compared with historical expectations. Specifically, the objectives are to estimate toxicity, disease free, progression free, event free and overall survival rates in patients treated with an alemtuzumab T cell depleted, reduced intensity preparative regimen followed by allogeneic hematopoietic transplantation; evaluate immune recovery following this reduced intensity allogeneic immunotherapy; develop an in vitro assay to allow patient individualized targeted dosing. The study population is HIV negative, adult patients who are not pregnant but have confirmed diagnosis of disease; must have Cancer and Leukemia Group B (CALGB) performance status (PS) 0, 1, or 2; must have a 3-6/6 human leukocyte antigen (HLA)-matched related donor or 8/8 (A, B, C, DRB1, DQ are the primary determinants) or better HLA-matched unrelated donor who is evaluated and deemed able to provide peripheral blood stem cells (PBPCs) and/or marrow by the transplant team. The target population of patients is those with a high chance of progressive lymphoid or myelomatous diseases, progressive myeloid diseases, marrow failure syndromes or myeloproliferative disorders.