Tacrolimus and Mycophenolate Mofetil as Post-Grafting Immunosuppression

Inclusion Criteria: * Patients with AML, ALL, CML, CLL, myelodysplastic syndrome (MDS), NHL, Hodgkin's disease (HD), paroxysmal nocturnal hemoglobinuria (PNH), hypoproliferative dysplasia with or without increased blasts, or myeloma, who are at significantly higher than usual risk for mortality from conventional myeloablative allogeneic SCT due to age or comorbidities: * Age ≥ to 50 years with AML or ALL in complete remission or with \<18% blasts in bone marrow * Age ≥ to 50 years with MDS or CML. * Age 16 to 75 years with lymphomas or myeloma, who have failed chemotherapy and are not candidates for an autologous transplant, or who have failed a prior autologous SCT. * Patients of any age with CLL or low-grade NHL. Patients with CLL and low-grade NHL need to have failed at least first-line treatment, with an alkylating agent, fludarabine or 2-chlorodeoxyadenosine (2-CDA), or anti-CD20 monoclonal antibody rituximab. * Patients of any age with marrow failure * Patients ≥60 years old will first be considered for an allogeneic stem cell transplant from a family member and will be offered an unrelated donor transplant only if no suitable family member, preferably an HLA-matched sibling, is available. * Patients with hematological malignancy relapsed after prior auto transplantation. * Patients at high-risk (\>60%) of relapsing after autologous transplantation for hematological malignancies may receive allogeneic transplant as "consolidative immunotherapy". Diagnoses include MM, non-HL, HL, AML, ALL and MDS. Minimal duration between auto and allo transplants is 4 weeks. * Patients of any age with hematologic malignancies treatable by allo SCT, who, because of pre-existing medical conditions or the disease itself (Fanconi anemia or PNH), are considered to be at significantly increased risk for transplant toxicity using high-dose transplantation regimens. * Patients with metastatic renal cell carcinoma. Must have include good performance status (Karnofsky score ≥ 60%), no active brain metastases, life expectancy of at least 6 months, absence of bulky liver metastases. Patients will be treated on other active disease-specific protocols when available. * Patients with other malignant diseases treatable with allogeneic SCT may be eligible for this protocol on a case by case basis, if approved by the principal investigator and the BMT attending physicians group. * Available HLA-identical, a one-antigen mis-matched sibling donor, a phenotypically HLA-matched family member, a phenotypically matched unrelated donor, or a 9/10 matched unrelated donor. * Age ≤ 75 years. Exclusion Criteria: * Patients with hematological malignancies eligible for a curative autologous SCT: intermediate- or high-grade NHL with chemo-sensitive first relapse. * HD with chemo-sensitive first relapse. * Otherwise healthy patients who are eligible for a conventional myeloablative allogeneic SCT. * Patients with rapidly progressive intermediate or high-grade NHL, unless in minimal disease state after the last treatment. * Patients with active uncontrolled CNS involvement with malignancy. * Fertile men or women unwilling to use contraceptive techniques during and for 12 months following treatment. * Females who are pregnant. * Patients who are HIV positive * Organ dysfunction * Left ventricle ejection fraction \< 35%. * DLCO \<35% of predicted, or receiving continuous supplementary oxygen. * Liver function tests: total bilirubin \>2x the upper limit of normal, and/or transaminases \>4x the upper limit of normal. * Karnofsky score \<50 for patients \< 60 years, or \<70 for patients aged 60 - 69 years * Creatinine clearance \< 60 ml/min. * Patients with hypertension that is poorly controlled on antihypertensive therapy. * Patients with a positive PRA or anti-donor T or B cell (+) will be considered for this treatment protocol only if no other option is available.