This study will evaluate the safety and effectiveness of a genetically engineered antibody, alemtuzumab (Campath[R]) on patients with myelodysplastic syndrome. MDS is made up of malignant stem cell disorders that can mean low levels of red blood cells-that is, anemia-and low counts of white blood cells and platelets. Patients with MDS are at risk for infection, spontaneous bleeding, and possible progression to leukemia, a cancer of bone marrow. Although bone marrow can produce some blood cells, patients with MDS experience a decrease in production of blood cells. Alemtuzumab recognizes specific types of white cells called lymphocytes and destroys them. This study will examine not only the usefulness of the medication but also the side effects in patients with MDS.