This study will examine the safety and effectiveness of stem cell transplantation for treating patients with sarcomas (tumors of the bone, nerves, or soft tissue). Stem cells are immature cells in the bone marrow and blood stream that develop into blood cells. Stem cells transplanted from a healthy donor travel to the patient's bone marrow and begin producing normal cells. In patients with certain cancers, such as leukemia and lymphoma, the donor's immune cells attack the patient's cancer cells in what is called a "graft-versus-tumor" effect, contributing to cure of the disease. This study will determine whether this treatment can be used successfully to treat patients with sarcomas.