Federal, state, county, and city governments and agencies are beginning to use Twitter to update constituents on what's going on.
A recent post on Silicon Alley Insider listed a number of federal Twitter sources (with more added in the comments), but a casual Twitter search for other government entities are using the social media service as well.
Coloradogov: Provides Internet-based, electronic government services to state and local Colorado governments.
RSSNewsmaster: Government Information Coordinator and digital services leader at the Utah State Library
UtahHive: We are the Utah State Library Digital Library Services Team and the community of publishers of government information.
Nebraskagov: The Official State Government Website for Nebraska
RichlandSC: Official twitterer for Richland County government, SC (state capital)
Shepherdsville: Shepherdsville (Ky.) City Government Updates