Here are research studies about Twitter:
Happiness is assortative in online social networks. Research finds that social networks resemble real-life networks in that participants seek others in similar psychological mood states. (link)
“On Twitter, Conservative (or Liberal) by Association,” New York Times article. Study found that people reveal their political leanings via their social graph. (NYTimes.com coverage)
Twitter, the year in review (published by Twitter.com)
Bibliography of research on Twitter and microblogging, curated by danah boyd (link to HTML).
Eight percent of online Americans use Twitter. Conducted by Pew Internet & American Life Project, Dec. 9, 2010. Survey. (link to study in HTML or PDF)
What is Twitter, a Social Network or a News Media? Haewoon Kwak, Changhyun Lee, Hosung Park, and Sue Moon
Proceedings of the 19th International World Wide Web (WWW) Conference, April 26-30, 2010, Raleigh NC (USA) (link to abstract, PDF, slide deck). Unobtrusive analysis.
Twitter in Higher Education 2010: Usage Habits and Trends of Today’s College Faculty Magna Publications (PDF on Scribd.com). Survey.