Donor Umbilical Cord Blood Stem Cell Transplant in Treating Patients With Hematologic Malignancies

Inclusion Criteria: * Patients will be diagnosed with one of the following hematological malignancies: acute myelogenous leukemia (AML), acute lymphoblastic leukemia, non-Hodgkin's lymphoma, myelodysplastic syndrome (MDS), chronic myelogenous leukemia (CML), and myeloproliferative and lymphoproliferative disorders * AML--First remission (CR1) with high risk features including a known prior diagnosis of myelodysplasia (MDS); therapy related AML; white cell count at presentation \> 100,000; presence of extramedullary leukemia at diagnosis; unfavorable AML subtype (M0, M5-M7); poor cytogenetic markers (abnormalities of chromosome 5, 7 or 8, 11q23, Philadelphia chromosome, complex karyotype) * AML--Second remission (CR2) or subsequent remission * AML--Relapse/Persistent Disease with \< 20% bone marrow blasts * ALL--First remission (CR1) at high risk for relapse as defined by: B cell ALL white blood cell count (WBC) at presentation \> 30,000 (T cell ALL WBC \> 100,000); presence of high-risk cytogenetic abnormality such as t(9;22), t(1;19), t(4;11) or other MLL rearrangements (11q23), t(8;14) * ALL--Second remission (CR2) or subsequent remission * ALL--Relapse/Persistent Disease with \< 20% bone marrow blasts * Non-Hodgkin Lymphoma--Induction failure or relapse and sensitive to most recent chemotherapy * MDS--Low or Intermediate-1 International Prognostic Scoring System (IPSS) score with: life-threatening cytopenia(s); and/or red cell or platelet transfusion dependence * MDS--ANC…