GRAFT-VERSUS-HOST DISEASE (GVHD) PROPHYLAXIS: Patients receive tacrolimus IV continuously (inpatients) or over 1-2 hours twice daily (BID) (outpatients) or orally (PO) BID on days -1 to +180 (patients receiving related or unrelated stem cells) or days -3 to +180 (patients receiving umbilical cord blood) with taper beginning on day +56 (related donor recipients) or +100 (unrelated donor or umbilical cord blood recipients) in the absence of GVHD. Patients also receive methotrexate IV on days +1, +3, +6, and +11 (related and unrelated donor recipients only) or mycophenolate mofetil IV or PO every 8 hours on days 0 to +40 with taper to day +96 (umbilical cord blood transplant recipients only).