Donor Stem Cell Transplant or Donor White Blood Cell Infusions in Treating Patients With Hematologic Cancer

OBJECTIVES: Primary * Determine the effectiveness of unrelated donor allogeneic hematopoietic stem cells for transplantation after conditioning for the treatment of patients with high-risk hematologic malignancies. * Compare survival, disease-free survival (DFS), response rate, and toxicity rates in these patients with historical controls. * Compare the rate and severity of acute and chronic GVHD after allogeneic hematopoietic stem cell transplantation in patients with hematopoietic malignancies with historical controls transplanted with stem cells from related sibling donors * Assess engraftment, long-term hematopoietic recovery, relapse rate, and disease-free survival when allogeneic hematopoietic stem cells are used as a source of stem cells for transplantation in patients with high-risk hematological malignancies. * Assess engraftment, long-term hematopoietic recovery, and overall survival when allogeneic hematopoietic stem cells are used as a source of stem cells for transplantation in patients who have graft failure or graft rejection. * Compare engraftment, long-term hematopoietic recovery, rate of GVHD, rate of relapse, toxicity rates, overall disease-free survival and overall survival when donor leukocyte infusions (DLI) are given for patients who have disease recurrence, progression, or low donor chimerisms after unrelated stem cell transplantation or before DLI with historical controls of other donor leukocyte infusions. Secondary * Determine the quality of life of patients undergoing hematopoietic stem cell transplantation or donor leukocyte infusions from unrelated HLA genotypically-identical donors. OUTLINE: Patients are assigned to 1 of 8 treatment groups. * Group 1\*: Patients undergo total body irradiation (TBI) twice a day on days -7 to -4. Patients then receive cyclophosphamide IV over 1 hour on days -3 and -2. On day 0 patients undergo stem cell transplantation (SCT). Beginning on day 7, patients receive filgrastim (G-CSF) IV once daily until blood counts recover. * Group 2 (patients who have previously experienced dose-limiting radiotherapy): Patients receive oral busulfan 4 times daily on days -7 to -4 and cyclophosphamide IV over 1 hour on days -3 and -2. On day 0 patients undergo SCT. Beginning on day 7, patients receive G-CSF IV once daily until blood counts recover. * Group 3 (pediatric patients only): Patients receive busulfan IV 4 times daily on days -9 to -6 and cyclophosphamide IV over 1 hour and fludarabine IV over 30 minutes on days -5 to -2. On day 0 patients undergo SCT. Beginning on day 7, patients may receive G-CSF IV once daily until blood counts recover. * Group 4 (second SCT for patients who have experienced graft rejection or failure)\*: Patients receive low-dose fludarabine IV over 30 minutes on days -4 to -2. Patients then undergo low-dose TBI once followed by SCT on day 0. Beginning on day 7, patients may receive G-CSF IV once daily until blood counts recover. * Group 5 (patients who developed grade 3 cystitis after prior cyclophosphamide-containing therapy): Patients receive carmustine IV over 2 hours on day -6, etoposide IV over 2 hours and cytarabine IV over 30 minutes on days -5 to -2, and melphalan IV over 30 minutes on day -1 (BEAM). On day 0, patients undergo SCT. Beginning on day 7, patients receive G-CSF IV once daily until blood counts recover. * Group 6 (cord blood transplantation): Patients receive anti-thymocyte globulin IV once daily and methylprednisolone IV twice daily on days -3 to -1. On day 0, patients undergo an umbilical cord blood SCT. * Group 7 (patients with relapsing or progressive disease after prior transplants or low donor chimerisms)\*: Patients must not have existing graft-versus-host disease (GVHD). Patients receive donor lymphocyte infusions with conditioning chemotherapy and/or radiotherapy at the discretion of the investigator. * Group 8 (pediatric patients only)\*: Patients undergo TBI twice a day on days -7 to -5. Patients also receive etoposide IV over 24 hours on day -4 and cyclophosphamide IV over 1 hour on days -3 and -2. On day 0, patients undergo SCT. Beginning on day 7, patients may receive G-CSF IV once daily until blood counts recover. NOTE: \*Patients who have received \> 3000 cGy to the central nervous system or \> 2000 cGy to the lung or liver may not receive any regimen containing total body irradiation (TBI) All patients receive GVHD prophylaxis comprising methotrexate IV on days 1, 3, 6, and 11; cyclosporine and/or tacrolimus on days -2 to 100; and/or methylprednisolone IV on days 7 to 100. Patients with an unrelated donor who experience a relapse prior to transplantation, may proceed directly to transplantation. However, if immediate transplantation from the unrelated donor is not possible, the patient must be re-induced into a complete hematological remission. Patients who experience graft failure or graft rejection after allogeneic transplantation are eligible for a second stem cell infusion from the original donor. Quality of life is assessed at baseline and at 7 days, 3 months, and 1 year after transplantation. After completion of study treatment, patients are followed periodically for survival. PROJECTED ACCRUAL: A total of 43 patients will be accrued for this study.