Examples of twitter fiction

Microfiction (or twisters -tales told in 140 characters or less)
Very Short Story
Arjun Basu
tweettales
microprose
twitterfiction

Nanoism - a paying twitterzine (twitlit magazine)

Twittories - collaborative short stories using twitter

Twitter novels (told in serial tweets)
Fuel Dump
Small Places
The Twitter Novel

Twitterature
Twitterature is an actual print book 'The world's greatest books retold through Twitter', there are examples here and you can follow the authors who are continuing to tweet their way through the literary canon here.