First... the Evercookie is a fun yet potentially nasty thing... it's very hard to get rid of...

evercookie is a javascript API available that produces
    extremely persistent cookies in a browser. Its goal
    is to identify a client even after they've removed standard
    cookies, Flash cookies (Local Shared Objects or LSOs), and
    others.

    evercookie accomplishes this by storing the cookie data in
    several types of storage mechanisms that are available on
    the local browser. Additionally, if evercookie has found the
    user has removed any of the types of cookies in question, it
    recreates them using each mechanism available.

    Specifically, when creating a new cookie, it uses the
    following storage mechanisms when available:
     - Standard HTTP Cookies
     - Local Shared Objects (Flash Cookies)
     - Silverlight Isolated Storage
     - Storing cookies in RGB values of auto-generated, force-cached 
        PNGs using HTML5 Canvas tag to read pixels (cookies) back out
     - Storing cookies in Web History
     - Storing cookies in HTTP ETags
     - Storing cookies in Web cache
     - window.name caching
     - Internet Explorer userData storage
     - HTML5 Session Storage
     - HTML5 Local Storage
     - HTML5 Global Storage
     - HTML5 Database Storage via SQLite

See the creator's site about the evercookie HERE

There are some solutions to defeating it, like usuing a virtual machine and deleting the instance of the virtual machine every time you are done browsing, then pasting a new instance over from a backup. Or... now there is a firefox plugin, however it's not free currently.

Anonymizer, Inc., a company that helps protect consumer’s privacy and offers anonymity solutions, announced today that it has developed Anonymizer Nevercookie, a free Firefox plugin that protects against the Evercookie, a javascript API built and made available by Samy Kamkar (same guy who brought you the Samy Worm and XSS Hacking to Determine Physical Location) who set out to prove that the more you store and the more places you store it, the harder it is for users to control a Web site’s ability to uniquely identify their computer. Nevercookie Plugin

The plugin extends Firefox's private browsing mode by preventing Evercookies from identifying and tracking users.

See the rest HERE