The Whois database is a free database that relays the information of the creater/owner of a domain name for a website. Many people use this database especially those that combat fraud and theft. Without this database, people that wanted to find out who the owner of a website is would most likely have to get a subpoena which would be costly and time consuming.
This database is getting a lot of speculation from privacy advocate groups. They believe that domain name owners should not have to disclose their information to the general public. This does make sense, however I don't believe it is necessary to eliminate this database in order to protect people that want to keep their information private. It is possible to register domain names through third parties who give you the option to keep your info private, for a price. I think this is a fine solution for the privacy problem.