OUTLINE: This is a randomized, multicenter study. Patients are stratified according to disease (acute myelogenous leukemia (AML) vs acute lymphocytic leukemia (ALL) or lymphoblastic leukemia (LL) vs myelodysplastic syndrome (MDS) or secondary AML vs chronic myelogenous leukemia (CML) vs non-Hodgkin's lymphoma vs multiple myeloma), stage of disease (if not CML, 1st complete response (CR) vs 2nd CR vs no 1st/2nd CR; if CML, 1st CR vs other phases), conditioning regimen (cyclophosphamide (CTX) and total body irradiation (TBI) vs busulfan (BU) and CTX vs other), source of donor (allogeneic vs autologous), T-cell depletion or autologous transplantation (no vs yes), and source of stem cells (bone marrow vs peripheral blood stem cell). Patients are randomized to receive a standard regimen or an intensified regimen. Standard pretransplant treatment: CTX on days -6 and -5 and TBI on days -4 through -2, or BU on days -8 through -5 and CTX on days -4 and -3, or BU on days -8 through -5 and melphalan IV on day -4. Intensified pretransplant regimens: I. Continuous infusion of idarubicin (IDA) over 48 hours on days -12 and -11, followed 5 days later with CTX on days -6 and -5 and TBI on days -4 to -2 II. IDA followed 5 days later with BU on days -8 through -5, and then CTX on days -4 and -3 III. IDA followed by BU on days -8 through -5 and melphalan IV on day -4. Stem cells are infused on day 0. Patients are followed every 3 months during the first 3 years, then every 6 months thereafter.