Writing (fiction) on Twitter is an idea that has fascinated me almost ever since I joined the service. I hadn't tried it before myself, but a little over a week ago I started to write a Twitter fiction. It's fun.
Although the length of writing is limited and photo and video sharing is growing online, the main content of Tweets is still written text. Writing skills help getting interest for your Tweets. On the other hand because of this Twitter as a writing platform or for supporting your writing efforts or marketing them makes sense.
There's lots of different sort of fiction available on Twitter. There are parody accounts for real people and real or already ended television shows. There are accounts that are set to support the story telling of a television show or some other, non-web-based story telling. And there are one Tweet long fiction or continuing stories (like mine).
Some use Twitter to continuously giving short tips around a subject, which could be seen as non-fictional writing. These sort of Tweets differ usually from other shared content and personal or more general Tweeting.
Different types of writers are also finding Twitter for their marketing efforts. Paulo Coelho is an easy example. He realized very early on the potential of social media for a writer.
Besides the novelists, bloggers are obviously very keen to use Twitter to promote their blog posts. Journalists are getting on with Tweeting as we speak and magazines and newspapers are roaming to Twitter.
I recommend any sort of writers to join Twitter and start writing away. The short format may seem limiting, but it has it's advantages: For instance it's a great way to learn to shorten and "compress" your writing.