Many non-profit CEOs or executive directors ask me about the use of Twitter, almost always with a smirk of skepticism. Would people really follow them? Outside the obvious event or fundraiser promotion - what would they tweet? While pushing content out to one's base is important - that's not the way to think about twitter.
It was relatively late in the game that Twitter made perfect sense to me - it's the ideal, no...perfect tool for knowing your customer base, competitors, donors, whatever population you're trying to keep a pulse on. It's not so much about the push (tweeting) as the pull (following). I use twitter daily to keep track of what's going on in several Boston industries - restaurant, education, museums, non-profit - any field where I have clients or wish to have clients. Precisely because of the short length of each message and the relative ease to publish it, people tend to publish thoughts, goals, small daily events that you can't get from following the trades and certainly aren't going to find out at that next mixer.
Select the people, businesses or organizations that you want or need to know and follow them. Not sure who to follow? See who others are following. Soon, you will have a collective pulse of what's going on around town (or further out if you choose) while also being seen as someone who's interested in that business or person....good basic customer relations management.