Removing your account is easy, although the link isn’t easily found. From their FAQ:
If you decide that you would no longer like to play on the Neopets site, you can remove your account.
To do this, make sure you are logged into the account you wish to deactivate, and then visit the remove account page (http://www.neopets.com/remacct.phtml) and enter your password.
You can also submit a ticket to remove your account by clicking on the “Request Support” tab.
URLS:
http://www.neopets.com
http://www.neopets.com/remacct.phtml
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.