This study will evaluate the safety and effectiveness of the experimental drug eculizumab for treating paroxysmal nocturnal hemoglobinuria (PNH), a disorder that can cause premature destruction of red blood cells. PNH may result in anemia requiring blood transfusions. Patients may be at high risk of life-threatening blood clots in their veins and may have urine discoloration, stomach pain, difficulty swallowing, tiredness, and poor quality of life. Men may have problems getting or maintaining an erection. Eculizumab is a monoclonal antibody that may improve the survival of red blood cells in patients with PNH.