Lee Aase, the social media manager at the Mayo Clinic (link to Twitter given the subject of this post), has posted six sensible reasons for an organization to get a Twitter account. It's short and worth reading.
I like this reason best: Listening and Engagement. The preceding reasons provide more than enough justification for getting a corporate Twitter account, but engaging stakeholders and listening to them is the best use for Twitter. For that reason, whether your boss approves a corporately branded Twitter account or not, I strongly suggest that you get your own personal Twitter account. Just dive in and start making connections. As you are using Twitter personally, you will see applications that are relevant to your work.