I've just read a three-page article in Writing Magazine about why writers should. It hasn't entirely convinced me mainly because I can't work out how you get followers.
That plus the fact I couldn't understand half of the so-called Twitter Basics, such as retweet and hashtags. The only bit I really grasped was the Fail Whale (shown when Twitter stops working).
Twitter should suit me as I'm a concise writer. I'm also a particular writer: I write and rewrite even my Facebook statuses in my head until I'm satisfied. (Usually.)
Perhaps I'll investigate a bit more.