You can’t delete your account yourself. Ask a staff member.
For more information, read this thread: http://www.zillow.com/advice-thread/Deleting-a-Zillow-account/470387/
Please note that AccountKiller.com is not associated with the business listed on this page. AccountKiller provides easy-to-understand instructions and guides on how to cancel charges and relationships from the list of businesses on our site, we have no affiliation with these businesses.