In this study, the investigators will utilize a regimen combining low dose total body irradiation and rabbit ATG to facilitate stem cell transplantation (SCT) with HLA matched related and unrelated donors. Based on the hypothesis that early treatment interventions have significant late effects in allogeneic SCT, a simple intervention, varying the duration of intense immunosuppression following SCT, will be investigated in this study. This may allow more robust recovery of donor immune system cells in the first two months following transplantation and eventually result in lower risk of cancer relapse, while maintaining effective graft versus host disease (GVHD) control. Patients will be randomly assigned to receive GVHD prevention therapy using one of two different immunosuppressive regimens with tacrolimus & mycophenolate mofetil (MMF). Patients assigned to the investigational group will receive MMF for 15 days following SCT with growth factor support using granulocyte macrophage colony stimulating factor (GM-CSF) beginning on post-transplant day 4. Patients randomized to the standard treatment group will receive MMF for 30 days following SCT with cytokine support using granulocyte colony stimulating factor (G-CSF) beginning on post-transplant day 4. If one of these treatment groups demonstrates an improvement in donor immune cell recovery, there may be a slow increase in the likelihood of patients being assigned to that more successful treatment group. Eventually the two groups will be compared with respect to the likelihood of either relapse or GVHD developing.