I use Twitter fairly regularly. Sometimes, it is a good way to find out what's going on around you. Of course, for this to work, we all have to use it and update it with new info - so I try to do that some, too. I've also found it useful in connecting internationally - makes for a cheap text message.
I've seen some pretty innovative uses of it. In DC, the streets department had a potholepalooza based on twitter, in which you could tweet the location of a pothole and they would come fix it. I once saw a pedestrian indicator that had been twisted around to the wrong way - I took a photo of it and tweeted it @ddot. They responded an hour later and the next day, it was fixed.