Non-Myeloablative Allogeneic Stem Cell Transplantation With Matched Unrelated Donors for Treatment of Hematologic Malignancies, Renal Cell Carcinoma, and Aplastic Anemia

Inclusion Criteria: * \<75 years old * Availability of suitable matched unrelated donor. We will require HLA matching at 9 of 10 loci including HLA A, B, C, DR and DQ. For patients treated at UCSF, typing will be done in the UCSF Immunogenetics Department. Typing will be done by high-resolution techniques at the allele level. Donors will be recruited through the National Marrow Donor Program (NMDP). Donors must meet the standards of NMDP as well as Institutional standards for donors at the center for which they are being collected. * Disease must be stable or responding to therapy. The expected time to disease progression should be greater than 12 weeks. * Disease types include: * Acute myeloid leukemia not expected to be curable with chemotherapy. This will include patients with high-risk cytogenetics (-7, -7q, -5, -5q, complex, Ph+), evolution from prior myelodysplasia or AML secondary to prior chemotherapy, failure to achieve remission, or second or subsequent remission. To ensure adequate time until disease progression, marrow blasts must be \<10%. This may be achieved using chemotherapy treatment. * Myelodysplasia with high-risk features. These will include adverse cytogenetics (-7, -7q, -5, -5q, complex), excess blasts, prior conversion to AML, or severe cytopenias, with ANC\<500uL or platelets \<20,000uL. Marrow blasts must be \<10%. This may be achieved using chemotherapy. * Acute lymphoblastic leukemia not expected to be curable with chemotherapy. This will include patients with high-risk cytogenetics (Ph+, 11q23 abnormalities, and monosomy 7), patients requiring more than one induction course to achieve remission, as well as patients failing to enter remission or in second or subsequent remission. Marrow blasts must be \<10%. * Chronic lymphocytic leukemia with high-risk features. This will include refractoriness to initial or subsequent therapy, progression after initial response to therapy, or prolymphocytic (PLL) morphology. * Follicular lymphoma with high-risk features. This will include refractoriness to initial or subsequent therapy, progression after response to initial therapy, or \> or equal 3 IPI risk factors. * Multiple myeloma, stage II-III. Patients are eligible either at diagnosis or after initial progression. * Other lymphomas including diffuse large cell lymphoma, mantle cell lymphoma, or Hodgkin's disease which as failed to respond to primary therapy, progressed or recurred after prior therapy. * Myeloproliferative diseases (myelofibrosis, polycythemia vera essential thrombocytosis) with evidence of disease acceleration. * Chronic myeloid leukemia with failure disease control by Imatinib. * Renal cell carcinoma with metastatic disease * Aplastic anemia not responsive to immunosuppressive therapy * Laboratory requirements (within 2 weeks of entry, EF and DLCO within 4 weeks): --Creatinine ,2.0mg/dL and creatinine clearance \>40 mL/min * Bilirubin \<3mg/dL, AST \<4x upper limit of normal. Patients with elevated total bilirubin who are suspected of having Gilbert's Disease will be eligible if the direct bilirubin is normal. * Patients with hepatitis C and hepatitis B are eligible if bilirubin and AST meet above criteria * Cardiac ejection fraction \>30% * DLCO \>40% predicted * Negative pregnancy test (for females of reproductive age) * Absence of uncontrolled active infection. * Prior stem cell (or bone marrow) transplantation is permitted * Signed informed consent Exclusion Criteria: * Active infection requiring ongoing antibiotic treatment * Poor performance status * Rapid progression of malignant disease * Opinion of BMT Committee that autologous transplant would be a preferable form of treatment * Organ function below requirements * Pregnancy