You can lookup an Amazon Wish List by searching for a person's name or email address under "Accounts & Lists." Here, you will find "Wedding Registry," "Baby Registry," and "Friends & Family Gifting" (for gift suggestions from existing lists or Facebook accounts).
You can request access to friends' wish lists via email if they have not already shared their personal (URL) link with you. "Accounts & Lists" > "Your Friends" > "Email the message." To lookup an Amazon wedding or baby registry hover over Accounts & Lists on the top right > Wedding Registry/Baby Registry > type in the name of the registrant or their email address and search. Make sure it is the correct list.
Once you see a list of suggested items you can either add to cart to buy at a later date or proceed to checkout. Amazon has since removed the public search for general wish lists.