In my opinion, the purpose of any web ring is to serve two groups of users: First, they help the website owners by bringing traffic to their sites—site visitors who are focused on the subject of the ring. Second, they help the site visitor by linking websites together with a common theme—the subject the site visitor is interested in.
Some web rings have a highly focused subject matter, for example The Wolf Webring is about Scott Cohen's portrayal of the character Wolf in the TV miniseries The Tenth Kingdom. And despite the highly focused subject matter it boasts seven member websites. At the opposite end of the spectrum is The Original Webring, which seems to be about anything, and boasts over 370 active websites.
I feel that if a webring has a focus, it should accept only member sites who share that focus or it risks not serving the two groups of users who depend on the ring.
I'm now managing the ActiveWorlds Webring, a ring with a focus. Websites must qualify for membership in this webring. However, qualification is easy.