The libraries that I looked at seemed to use Twitter in a variety of ways. Some of these were:
Tweets about new and/or interesting titles just received or of note
Tips on how you can use the library services more effectively (eg sending in an online suggestion for purchase)
Comments about news items of interest, often with links to articles or other websites (All Whites, Witi Ihimaera, New moon movie)
Events coming up
Other Twitter users definitely appeared to be interacting with the libraries, and most of the tweets were in a fairly informal, chatty style.
I think on the whole I personally would be more likely to follow tweets with some sort of information or news in them, especially where they included links to articles of interest and other websites. I guess with an instution like a library you're less likely to get the sort of stuff that would be sent between friends and people who really know each other well and understand each other's terminology and are interested in what their friends are thinking, feeling or doing at any particular time. I do agree with a comment I read in one of the articles about Twitter and libraries which said that even if you don't think Twitter is terribly applicable right now, it pays to keep up with the latest technology anyhow, and know what's out there. Which is where I'm coming from in doing this course - not that keen on using Twitter myself but at least I now have a vague idea what it's all about!
OK, here's my attempt at a 'tweet':
A great read if you like cricket: Michael Simkins' book 'Fatty batter' will have you laughing out loud!