Truthfully, most of the stuff on Twitter is less than interesting to me. Plenty of banality. But taken en masse, those messages start to get pretty fascinating. Of course I'm glued there whenever there's something momentous happening (watching the protests in Iran unfold recently - heartbreaking). It can be used as a real-time search engine - when Facebook went down for several hours recently, it was sort of hilarious to search through tweet bemoaning this fact.
But all that data can be used for other things too. For instance, here's a very cool research project on the collective mood of the US throughout a 24-hour cycle as determined by Twitter posts.
Also, there ARE a few feeds that are genuinely creative/interesting.
Some funny/generally awesome Twitter accounts I've found
lowflyingrocks - Automatically generated Twitter stream detailing all objects that pass w/in .2 AU of Earth. Just kind of cool for the astronomy nerd in me. When that big Armageddon asteroid shows up, I'll be ready!
HalfPintIngalls - yep, it's "Laura Ingalls" tweeting away. Pretty snarky and hilarious.
feministhulk - HULK SMASH PATRIARCHY! Smart, thoughtful, AND funny. So great!
cookbook - recipes in 140 characters or less. Tricky to read at first, but tasty and simple to remember once you decipher them.
So many more of these. Dig around. Whatever your interest, there's probably someone tweeting about it.
Finally, a bit about libraries and Twitter
Twitter is an easy application to use/update, and in my opinion, it's worth it for libraries to at least TRY having a Twitter account to see what happens. But it's also important to realize that 1) not every cool tool will pan out the way you expect and 2) that's OK! It's not so much about finding the magic bullet as it is about trying things and seeing what sticks.
Leigh Anne Vrabel, a librarian at the Carnegie Library of Pittsburgh, writes here about her library's experiment with Twitter, and why it's been abandoned for the time being. Very thoughtful, worth a read.