Combinations of high-dose chemotherapy and radiation therapy (preparative regimen) followed with allogeneic bone marrow or stem cell transplantation from an unrelated donor is a current treatment approach. Chemotherapeutic drugs and radiation are given in higher doses to increase their effectiveness. High-dose chemotherapy and radiation therapy generally affect cells that are dividing. They are used to treat cancer because cancer cells divide more often than most other cells. High-dose treatment severely damages the patient's bone marrow so that the patient no longer is able to produce needed blood cells. Peripheral stem cell transplantation allows stem cells that were damaged by treatment to be replaced with healthy stem cells that can produce the blood cells the patient needs. Patients experience a number of complications after transplantation. Some are temporary and relatively minor; yet others can be life threatening. Many doctors consider high-dose chemotherapy, by itself or with radiation, and bone marrow or stem cell transplantation as the best available treatment option for diseases under specific circumstances. However, this study will explore whether a less-intensive preparative therapy before the peripheral stem cell transplantation will prove to be safer, have less side effects, and be an effective treatment for certain diseases.