When evaluating patients for unrelated donor transplant, the higher degree of matching, the lower risk of GvHD; the A, B, C, DRB1 and DQB1 loci, comprising 10 possible antigen (with alleles), will be typed for all unrelated transplants; given the higher risk of TRM in mismatched transplants, RIT is often the best way to mitigate the risk; data from the National Marrow Donor Program makes it possible to estimate the risk of donor-recipient HLA mismatch at the allele or antigen level; the higher risk from HLA-mismatching must be balanced against the clinical urgency and the patient's risk by the transplant team; at this time, antigen level mismatches at DQB1 do not affect outcomes and will not be used for matching purposes for donor selection; thus, the matching required will be at the HLA A, B, C and DRB1 (8 loci); for this protocol, a single antigen mismatch at the HLA A, B, C, with or without additional single allele level mismatch may participate in this protocol for voluntary unrelated donors (blood or marrow) DONOR: Donor must be healthy and have non-reactive test results for all infectious disease assays as required by state and federal regulations; donors who screen seropositive for hepatitis an/or syphilis must be cleared by infectious disease consultation DONOR: Donor must have no uncontrolled cardiopulmonary, renal, endocrine, hepatic or psychiatric disease to render donation unsafe DONOR: The donor (or parent in minor) must give informed consent for peripheral blood stem cell collection or bone marrow collection DONOR: Syngeneic donors are not eligible DONOR: Donors who have poor peripheral venous access, may require central venous line placement for stem cell apheresis