Are webrings still worth it these days or did they go out of style in the late 90's? Can joining a webring adversely affect your search engine ratings?
I don't think most are very helpful nor harmful. I don't see any way they could affect SE ratings (and certainly haven't observed such an effect)... maybe it could hurt if sites in the ring were unrelated, but that wouldn't be a very good webring. I'd say they give a site an unprofessional feel. That's fine sometimes of course. I use a webring for a site that's specific to a particular hobby, to link it in with similar sites.
If you want to look professional they are definitely not worth it. They were amateur in web 1.0. In web 2.0 they are just pathetic. BUT, if you run one is a good way to get a lot of links to your website as you can easily make every ring member link to your site with the code you provide them to be in the ring.