I signed up for a Twitter account (which I've since deactivated) when I attended a jQuery conference in Boston a few years ago. The live tweets that went around were not only hilarious, but also relevant to the discussions. In addition, I started following some developers and discovered some great links via tweets (for instance, Paul Irish tweeted his coding standards a while back, which I think is a great read for any developer and their team. http://na.isobar.com/standards/)

Do I think Twitter is a requirement for being a web developer? Definitely not. I agree with you (and voted you up.) But, I do believe, if you follow the right people, it will help you become a better one.

My only reason for deactivating it was because of Hacker News (and other aggregate sites) - A lot of the great content on Twitter ends up (or begins) on sites like HN.