Anononymity on a Web Site

Not unless you do somerthing dumb like give it to them on registration or do something illegal. If you do something illegal, then they can obtain an IP ( web address) from your ISP and then from their trace it can be traced back to you and perhaps get email address that way.

Websites can be created to search your computer for information which is why it is best to have spyware and virus protection as well as windows updates installed.