Our National Library use Twitter with a great deal of humour. Their tweets are short and pithy and when you see the photos they are commenting on you find that they have enhanced what is often quite a dated boring image. They caught my interest so that I would want to follow them.
The British Library uses their Twitter account to communicate with their followers things like their annual report being published and up and coming exhibitions. URLs in their tweets often link to a more in depth article about the topic. They have lots of followers who contribute. Some amazing photos.
Dunedin Public Libraries uses their Twitter account to inform the public of what is happening in the libraries. They have now over 500 tweets. The lighthearted comments make it an attractive account to follow.