In case you've got your new site and you're looking to promote it here and there, forget the concept of Web Rings. They are just about useless these days, and really weren't worth all that much back in the day.1 – They're a very old-school method of website promotion. They haven't kept up with the dynamic changes in the web.
2 – Even back when they "worked", they could only deliver maybe 10 clicks a day, but were highly prone to unfair abuses by unscrupulous webmasters.
3 – A couple clicks won't do you any good, but the code used may goof up your site's templates.
4 – If you have a blog, sign up for Technorati. It's better and smarter than Web-Rings.
5 – Join DMOZ.org by getting linked and listed in the appropriate category. You'll get as much traffic and even more links around the web.
Web Rings were a good idea, but they never really caught any traction, and never much worked in the first place. Today, you'll be lucky if you can consider it a joke.