Patients receive a conventional myeloablative conditioning regimen consisting of high doses of cyclophosphamide, busulfan, and etoposide, with or without total-body irradiation. Depending on the preparative regimen selected, the conditioning of recipients will take a total of 6 to 7 days. On day 0, patients will receive filgrastim (G-CSF)-mobilized HLA-matched, related, or unrelated donor allogeneic peripheral blood stem cells (unmanipulated). Patients will receive standard graft-vs-host disease prophylaxis consisting of cyclosporine or tacrolimus and methotrexate or sirolimus. Patients will receive rasburicase IV over 30 minutes, beginning on the first day of conditioning therapy, for 5 consecutive days. If after 5 days of rasburicase the patient's uric acid plasma level remains above 5 mg/dL, rasburicase may be continued for up to 7 days in total.