Melphalan, Fludarabine, and Alemtuzumab Followed by Peripheral Stem Cell Transplant in Treating Patients With Hematologic Cancer

INCLUSION CRITERIA: * Disease criteria: This trial is primarily designed for: 1) patients with relapsed or primary refractory non-Hodgkin's lymphoma, 2) chemosensitive relapsed or refractory acute and chronic lymphocytic leukemias, 3) relapsed or primary refractory Hodgkin's Disease, or advanced (Durie-Salmon stage II or III) multiple myeloma, advanced Waldenstrom macroglobulinemia, who, by virtue of advanced age, intensity of prior radiation and/or chemotherapy, history of prior toxicity associated with chemo/radiotherapy or existing organ dysfunction, would be at undue risk of regimen associated mortality if transplanted according to protocols involving myeloablative conditioning regimens. * Patients with aggressive NHL histologies must have chemo/radiosensitive disease, or have non-progressive disease, or have stable disease on therapy, and be ineligible for an autologous HSC transplant because of disease in the marrow. * Patients with chronic myeloid leukemia and high risk forms of acute myelogenous leukemia or myelodysplastic syndromes are also eligible in the absence of an alternative active higher priority allogeneic transplant protocol for which they are eligible. * Age criteria: Patients may be up to 70 years of age. There is no lower age threshold. Patients above the age of 70 may also participate, after evaluation and approval by the BMT Service attendings. * Absence of active or uncontrolled bacterial, viral, or fungal infection that would contraindicate the use of myelosuppressive chemotherapy. * Patients must have a healthy HLA-compatible donor, either a matched or single HLA allele disparate related donor or a similarly compatible unrelated donor recruited through the National Marrow Donor Program. Related donors must be willing to participate as research subjects and be willing to receive G-CSF to mobilize PBPC and undergo leukapheresis to donate PBSC. Unrelated donors identified by the NMDP may elect to donate either PBSC after treatment with G-CSF, or bone marrow. These unrelated donors will provide informed consent and their PBSC or bone marrow donations will be obtained at a qualified donor center participating in the NMDP. * Each patient must be willing to participate as a research subject and must sign an informed consent form after discussion of the nature and risks of the study prior to entering the protocol. Parents or legal guardians of patients who are minors will sign the consent form for these patients after discussion of the nature and risks of the study. EXCLUSION CRITERIA: * Female patients who are pregnant or lactating. * Active or uncontrolled viral (including HIV-1), bacterial or fungal infection. * Severe renal insufficiency (creatinine \>2.0 or creatinine clearance \< 30mL/minute) * Severe hepatic dysfunction, as defined by: total bilirubin greater than 2.5 mg/dL and AST and ALT \>3xnl, unless the liver is involved with disease. * Severe cardiac insufficiency, defined as a resting left ventricular ejection of less than 30% as measured by echocardiography or radionuclide cardiac angiography. Patients on cardiac medications for congestive heart failure are eligible, as long as their LVEF is greater than 30% on medication. * Severe pulmonary insufficiency, as defined by an adjusted diffusing capacity of less than 40% of predicted value. * Karnofsky or Lansky score \<40%