Amazon Customer's Privacy Exposed In theory, your Amazon wish list should allow people to buy you gifts, but should not reveal anything but the list of items you want.
Evidently, if you buy something for someone off their list, you can then see the delivery address in the order reports in your account.
Solution is to remove the delivery address from your list. Your friends and family would have to enter the delivery address manually, but one hopes that they already know it. A good description of the process is in the above linked article.