Brief Summary: 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. Patients between 4 and 35 years of age with a sarcoma that has spread from the primary site or cannot be removed surgically, and for whom effective treatment is not available, may be eligible for this study. Candidates must have been diagnosed by the age of 30 at the time of enrollment. They must have a matched donor (usually a sibling). Participants undergo the following procedures: Donors: Stem cells are collected from the donor. To do this, the hormone granulocyte colony stimulating factor (G-CSF) is injected under the skin for several days to move stem cells out of the bone marrow into the bloodstream. Then, the cells are collected by apheresis. In this procedure the blood is drawn through a needle placed in one arm and pumped into a machine where the stem cells are separated out and removed. The rest of the blood is returned to the donor through a needle in the other arm. Patients: For patients who do not already have a central venous catheter (plastic tube), one is placed into a major vein. This tube can stay in the body the entire treatment period for giving medications, transfusing blood, , withdrawing blood samples, and delivering the donated stem cells. Before the transplant procedure, patients receive from one to three cycles of "induction" chemotherapy, with each cycle consisting of 5 days of fludarabine, cyclophosphamide, etoposide, doxorubicin, vincristine, and prednisone followed by at least a 17-day rest period. All the drugs are infused through the catheter except prednisone, which is taken by mouth. After the induction therapy, the patient is admitted to the hospital for 5 days of chemotherapy with high doses of cyclophosphamide, melphalan, and fludarabine. Two days later, the stem cells are infused. The anticipated hospital stay is about 3 weeks, but may be longer if complications arise. Patients are discharged when their white cell count is near normal, they have no fever or infection, they can take sufficient food and fluids by mouth, and they have no signs of serious graft-versus-host disease (GVHD)-a condition in which the donor's cells "see" the patient's cells as foreign and mount an immune response against them. After hospital discharge, patients are followed in the clinic at least once or twice weekly for a medical history, physical exam, and blood tests for 100 days. They receive medications to prevent infection and GVHD and, if needed, blood transfusions. If GVHD has not developed by about 120 days post transplant, patients receive additional white cells to boost the immune response. After 100 days, follow-up visits may be less frequent. Follow-up continues for at least 5 years. During the course of the study, patients undergo repeated medical evaluations, including blood tests and radiology studies, to check on the cancer and on any treatment side effects. On four occasions, white blood cells may be collected through apheresis to see if immune responses can be generated against the sarcomas treated in this study. Positron emission tomography (PET) scans may be done on five occasions. This test uses a radioactive material to produce images useful in detecting primary tumors and cancer that has spread.

Detailed Description: Background: * Treatment of pediatric sarcomas has enjoyed progress in the past 25 years for patients with localized, chemosensitive disease and prognostic factors are now available to identify subsets of patients who have very dismal prognoses; patients with primary metastatic disease, especially those with bone and bone marrow metastases. * Patients with primary chemoresistant disease and early recurrence also have very poor prognoses and lack suitable treatment options. For these patients, it is critical that alternative approaches to cytotoxic chemotherapy be identified. * Basic laboratory studies have shown that Ewing's sarcoma is susceptible to immune mediated mechanisms of cytolysis in vitro. Interestingly, for Ewing's sarcoma this appears to be true for both chemosensitive and chemoresistant cell lines. * Recent progress in the field of bone marrow transplantation has identified approaches that can reproducibly induce allogeneic peripheral blood stem cell engraftment in adults with hematologic malignancies. In some cases, this same approach has shown beneficial effects for patients with solid tumors as a result of the development of allogeneic, immune-mediated graft versus tumor effects. Objectives: * To determine if the transplantation of human leukocyte antigen (HLA) matched, peripheral blood stem cells can result in full donor engraftment (greater than 95 percent by day 100) in patients with high risk-pediatric sarcomas. * To identify and characterize the toxicities of HLA-matched peripheral blood stem cell transplant (PBSCT) in patients with high-risk pediatric sarcomas. In particular we will identify the incidence of graft versus host disease (GVHD) and the pace of immune reconstitution in this population. * To determine if allogeneic graft-versus-tumor responses following allogeneic PBSCT can induce clinically significant anti-tumor effects as measured by radiographic evidence of antitumor responses following PBSCT in patients with measurable disease and improved clinical outcome compared to historical controls in this patient population with a universally poor outcome. Eligibility: * Patients, age of greater than 4 years at enrollment to less than 30 years at diagnosis and age less than 35 at enrollment, with ultra-high risk Ewing's sarcoma family of tumors, desmoplastic small round cell tumor or alveolar rhabdomyosarcoma. * Patients must have completed standard front-line therapy and salvage therapy. * Patient must have the availability of a 5 or 6 antigen HLA-matched first-degree relative donor or a genotypically identical twin. * Patients must have adequate cardiac, pulmonary, renal, liver, and marrow function. Design: -Donor will be prepared for peripheral blood stem cell harvest with Filgrastim mobilization, 10 microg/kg per day subcutaneous (SQ) for 5-7 days until they have stem cell collected by apheresis. The stem cells will then be cryopreserved. Patients will receive 1 to 3 21 day cycles of Fludarabine-EPOCH induction chemotherapy. The preparative regimen will consist of cyclophosphamide, fludarabine and melphalan followed by stem cell infusion. GVHD prophylaxis will consist of sirolimus and tacrolimus.