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.