This study will examine the safety and effectiveness of alemtuzumab (Campath® (Registered Trademark)) for improving muscle strength in patients with sporadic inclusion body myositis (s-IBM). The most common inflammatory muscle disease in people over the age of 50, s-IBM progresses steadily, leading to severe weakness and wasting of the muscles in the arms and legs. The cause of s-IBM is not known, but it may be an autoimmune disease, in which the body's immune cells (white blood cells) attack and destroy parts of muscle. Alemtuzumab is a laboratory-made antibody currently approved to treat certain leukemias. It has also been used to treat patients with autoimmune conditions such as rheumatoid arthritis, vasculitis, multiple sclerosis, and tissue rejection associated with transplantation. Alemtuzumab destroys white blood cells that have a protein called CD52 on their surface and that might be among the cells attacking muscle.