Donor Peripheral Stem Cell Transplant, Fludarabine, and Busulfan in Treating Patients With Hematologic Cancers

DISEASE CHARACTERISTICS: * Diagnosed with any of the following: * Acute myeloid leukemia (AML), meeting 1 of the following criteria: * Recurrent disease in remission, defined as morphological remission with bone marrow aspirate/biopsy showing ≤ 5% within 4 weeks before the start of study treatment (cytogenetic or molecular remission is not required) * In first complete remission (CR1) with poor-risk cytogenetics, antecedent hematological disease (i.e., myelodysplasia), or treatment-related leukemia * Acute lymphoblastic leukemia (ALL), meeting 1 of the following criteria: * Recurrent disease in remission, defined as morphological remission with bone marrow aspirate/biopsy showing ≤ 5% within 4 weeks before the start of study treatment (cytogenetic or molecular remission is not required) * CR1 with Philadelphia chromosome or poor-risk cytogenetics * Chronic myelogenous leukemia (CML), meeting the following criteria: * First or second chronic phase * Must be documented disease progression after imatinib mesylate therapy OR documented lack of cytogenetic response 6 months post-imatinib mesylate initiation OR imatinib mesylate intolerance * Chronic lymphocytic leukemia (CLL), meeting the following criteria: * Recurrent disease after fludarabine-based therapy * Must have chemosensitive disease at the time of relapse, defined as greater than 50% reduction of WBC and lymphadenopathy * Recurrent Hodgkin lymphoma, recurrent non-Hodgkin lymphoma (NHL) (low-, intermediate-, or high-grade disease\*), or transformed NHL, meeting 1 of the following criteria: * Received prior autologous transplantation and cytoreductive therapy at the time of relapse to achieve complete remission (CR) or CR/unconfirmed (CRu) as defined by the International Workshop * Relapsed disease that required more than 2 salvage regimens to achieve CR or CRu * Recurrent multiple myeloma, meeting the following criteria: * Must have received prior autologous transplantation and demonstrate chemosensitivity at the time of relapse, defined as greater than 50% reduction of M-component or plasma-cell marrow infiltration * Myelodysplastic syndrome * Refractory anemia (RA)/RA with ringed sideroblasts (RARS), refractory cytopenia with multilineage dysplasia (RCMD)/refractory cytopenia with multilineage dysplasia with ringed sideroblasts (RCMD-RS), or RA with excess blasts (RAEB) I, meeting the following criteria: * Must be transfusion-dependent and have an IPSS score ≥ 1.5, based on WHO criteria * No RAEB II or del(5q) * No uncontrolled CNS metastases * 5-6/6 HLA-matched sibling or 9-10/10 matched unrelated donor (both patient and donor) available PATIENT CHARACTERISTICS: * Karnofsky performance status ≥ 50% * Serum creatinine ≤ 2 mg/dL * Not pregnant * Fertile patients must use effective contraception * 50 years of age or older * Patients 18-50 years of age are eligible if meeting 1 of the following criteria: * Have a preexisting medical condition * Received prior therapy (i.e., autologous transplantation) and are considered to be too high risk for conventional myeloablative transplantation * Must be willing to accept or comprehend irreversible sterility as a side effect of therapy * No uncontrolled active infection * No psychiatric illness or mental deficiency making compliance with treatment or informed consent impossible * Cardiac ejection fraction ≥ 30% * Corrected pulmonary-diffusing capacity ≥ 35% * No serologic evidence of infection with HIV * No decompensated liver disease with serum bilirubin \> 2.0 mg/dL PRIOR CONCURRENT THERAPY: * See Disease Characteristics