I set up a twitter account for our library (@camdencclibrary) a little more than a year ago as a bit of an experiment, and 355 tweets later -- admittedly not much in the land of twitter -- I still think it's a good idea, and that it's important to be there.
First and perhaps foremost, the speed of the service is amazing. This can be invaluable for world, local, and professional news and information. Often when people are faced with the overwhelming information landscape, whatever they can access the quickest trumps all else, including quality. (I used to think this was laziness, but now I think of it more as a coping mechanism.) This makes twitter relevant to librarians as information providers, but it is also relevant to librarians as information consumers, because if your network is good enough any information you could want is at your finger tips in ways that can be smarter than google.
If you miss information in real time, a twitter search is also a valuable tool for asynchronous communication. If you are looking for solutions to technical problems, or synopses of conferences or events, it can be really useful to go back and see if anyone else is struggling with the same questions or is on the same wavelength.
The messages on twitter are continually being aggregated, and thanks to the large community of people using the service, this often reveals meaningful patterns. Even if it doesn't seem that anyone is reading your messages, the words you are using contribute to a rich network of trends.
Having said all this, I have some caveats:
Your twitter account is only as good as the people and organizations you are following, and those who are following you. If your contacts are the types of people who share the minutiae of every waking moment, your experience with twitter may be completely vapid.
And as is true for many endeavors, a twitter account requires maintenance. I have noticed that when I am extremely busy I allow other things to take precedence over it, and only when things slow down enough again do I go back to it. I don't think this is entirely bad, as it functions like any other online community in this way; never too far away, and always waiting for you.
Consistent with lots of things on the web, twitter is constantly changing. It can sometimes be hard to see through the hype, and who knows what clever uses people will come up with for it next, but as a tool for informal, flexible, and fast communication, it's pretty darn neat.