|Inclusion Criteria:||1) Diagnosed with one of the following diseases:|
2) Acute myelogenous leukemia (AML) in induction failure, relapse, past first remission, or CR1 considered at risk for relapse
3) Myelodysplastic syndromes with International Prognostic Scoring System score (IPSS score) >/= 2 or myelodysplasia that has not responded to chemotherapy
4) Biphenotypic leukemia
5) Acute lymphocytic leukemia with induction failure, first complete remission with high risk cytogenetics (e.g. Philadelphia positive chromosome, t(4:11) Remission requiring more than 2 chemotherapy to achieve remission, or any stage beyond CR1
6) Chronic Myelogenous Leukemia (CML): second chronic phase, accelerated phase or blast crises with less than 10% blasts in the bone marrow, or CR1 and resistance to Gleevec or other tyrosine kinase inhibitors
7) Non-Hodgkin's Lymphoma - induction failures, second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant)
8) Hodgkin's disease - induction failure, second or later complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant).
9) Chronic Lymphocytic Leukemia that has failed induction therapy or Rai Stages 2-4
10) Related or unrelated donor which is HLA-matched or mismatched in 1 HLA A, B, C, DR, or DQ locus is acceptable (i.e. >/= 9/10 matched related or unrelated donor, matched with molecular high-resolution technique per current std. for BMT program). Cord blood units must match patient at 4, 5, or 6/6 HLA class 1 serological & II molecular antigens with a min. of 2 x 10e7 TNC/kg recipient weight in the pre-thawed fraction. For patient lacking a matched related or unrelated donor or acceptable cord blood unit(s), a related haploidentical donor (</= 7/8 allele matched at A, B, C, DR loci) may be used.
11) Age </= 60 years.
12) Lansky performance score >/= 50% for patients </= 16 years of age, or Zubrod performance status score of 0-2 for patients > 16 years of age.
13) Cardiac function - left ventricular ejection fraction >/= 40%.
14) Pulmonary function - diffusion capacity of at least 50% predicted. Children unable to perform pulmonary function tests (e.g. less than 7 years old) pulse oximetry of >/= 92% on room air.
15) Serum creatinine < 1.6 mg/dL or creatinine clearance >/= 50 ml/min.
16) SGPT </= 200 IU/mL, serum bilirubin < 1.5 x normal.
17) Written informed consent and assent as is age appropriate.
18) No active infection.