The purpose of this study is to evaluate the ability of sirolimus to prevent graft versus host disease (GVHD) in patients following stem cell transplant from an unrelated donor. This trial is designed to test the hypothesis that elimination of methotrexate in the unrelated donor group would lead to less transplant-related toxicity while still preserving the effective control of GVHD.

• Therapy to prevent GVHD will consist of an infusion of tacrolimus intravenously and sirolimus orally once daily starting 3 days before stem cell infusion. This will take place in the hospital where the patient will remain for the duration of the transplant.
• Sirolimus will continue for approximately 100 days at a stable dose, then it will be tapered slowly over the course of weeks to months to prevent a flare in GVHD.
• Patients will be seen in the clinic weekly for the first 2 months after discharge from the hospital. If GVHD is present, tapering schedule will be slower and based on the patient's clinical condition.
• Tacrolimus will also be given orally after the patient is discharged and will be tapered on the same schedule as sirolimus.
• During the year following stem cell transplant, blood tests will be performed to evaluate the immune system and graft versus host disease.

Inclusion Criteria:

• Acute myelogenous leukemia(AML) in first or subsequent remission, in untreated first relapse or any treated relapse.
• Acute lymphoblastic leukemia(ALL) in first or subsequent remission, in untreated first relapse or any treated relapse.
• Chronic myelogenous leukemia in first or second chronic stable phase or in accelerated phase.
• Myelodysplastic syndromes or myeloproliferative diseases
• Non-Hodgkin's lymphoma or Hodgkin's disease in second or greater complete remission, in partial remission, or induction failure.
• Chronic lymphocytic leukemia, Rai stage 2-4, which has progressed after initial therapy.
• Matched unrelated donor.
• Age 18-55 years at the time of stem cell transplantation
• ECOG performance status 0-2
• Life expectancy of 100 days without stem cell transplantation
• Total bilirubin < 2.0 mg/dl
• AST < 90 IU
• Serum creatinine < 2.0 mg/dl
• Ejection fraction > 40% by echocardiogram or gated nuclear medicine study.

Exclusion Criteria:

• Uncontrolled infection
• Forced vital capacity or DLCO < 50% predicted for age
• Uncontrolled hypertension
• Prior hematopoietic stem cell transplant
• Evidence of HIV infection or active Hepatitis B or C infection
• Cholesterol > 300 mg/dl
• Relapsed aggressive Burkitt's or Burkitt's-like lymphoma