Wow - that site really is bad.
Anyway from this FAQ article you need to do the following:
How do I delete my account?
To delete your WebRing account, you
must first quit any WebRing Commuities
(rings) in which you are a member. To
do this, follow these steps:
- Log into WebRing and view your My Account page.
- Scroll down and click the Memberships tab to open the list of
your ring memberships.
- Click on your Site Title(s) to bring up the Edit Site Information
page.
- Find and click the "Delete Site from Ring" link in the left column of
that page.
- Repeat this process until you have deleted your site(s) from all the
rings you belong to. (There is no way
to do this for all rings at once. It
must be done one ring at a time.)
If you manage any rings, you must
dispose of them. You may transfer
management to another member of the
ring, or to some other WebRing member,
or you may delete a ring that has no
members.
Once all your memberships are deleted,
you will find the "Delete This User
ID" link in the left column of your My
Account page. Once you click that
link, you will end your membership in
WebRing.