These govermental bodies' Web pages are not only interesting in their own right, but also provide many great links to a variety of other weather resources on the net.
Obviously, the National Weather Service (NWS) itself is a great place to begin. Be sure to check out IWIN - the Interactive Weather Information Network, a new NWS feature, for reports, forecasts, and severe weather watches and warnings too. Then there is its parent agencyof the NWS, the National Oceanic and Atmospheric Administration (NOAA).
For those who are interested in nature at its worst there are the National Severe Storms Laboratory and the Storm Prediction Center in Norman, Oklahoma. And, for hurricane information, there's the National Hurricane Center in Miami, Florida. Finally, there is the NWS Fire Weather Program which focuses on the Western US.
In the area of Climatology, check out the National Climatic Data Centerand specifically its interactive CLIMVIS system. A related resource is the Climate Prediction Center. [Regional climate data is available from the Climate menu selection]
For international audiences, here are some other governmental sites: From our neighbours to the north, there is Environment Canada operates The Weather Office, in Great Britain there is The Met. Office, and for a world-wide perspective, there's the World Meteorological Organization, with headquarters in Geneva, Switzerland.