This study will examine the use of etanercept (also called Enbrel or TNFR:Fc) in patients with Wegener's granulomatosis, a type of vasculitis (blood vessel inflammation). Wegener's granulomatosis may affect many parts of the body, including the brain, nerves, eyes, sinuses, lungs, kidneys, intestinal tract, skin, joints, heart, and other sites. Generally, the greater the disease involvement, the more life-threatening it is. Standard treatment is a combination of prednisone and a cytotoxic agent-usually cyclophosphamide or methotrexate. However, many patients treated with this regimen have a disease relapse, and others cannot take these drugs because of severe side effects. This study will evaluate etanercept's safety and effectiveness, and particularly its value in reducing the need for prednisone and preventing disease relapse.