People with Fabry disease have an alteration in their genetic material (DNA) which causes a deficiency of the a-galactosidase A enzyme. Fabrazyme is a drug that helps to breakdown and remove certain types of fatty substances called "glycolipids." These glycolipids are normally present within the body in most cells. In Fabry disease, glycolipids build up in various tissues such as the liver, kidney, skin, and blood vessels because a-galactosidase A is not present, or is present in small quantities. The build up of glycolipid ("globatriaosylceramide" or "GL-3") levels in these tissues in particular is thought to cause the clinical symptoms that are common to Fabry disease. This study will test the safety and efficacy of Fabrazyme in the treatment of patients with Fabry disease.