Among the programs run by the NWS is SKYWARN. Unlike many Federal programs which embrace a very top-down approach, the SKYWARN program relies of local volunteers to report dangerous weather. From the official description:
The effects of severe weather are felt every year by many Americans. To obtain critical weather information, NOAA's National Weather Service (NWS), part of the U.S. Department of Commerce, established SKYWARN with partner organizations. SKYWARN is a volunteer program with over 230,000 trained severe weather spotters. These volunteers help keep their local communities safe by providing timely and accurate reports of severe weather to the National Weather Service.
Although SKYWARN spotters provide essential information for all types of weather hazards, the main responsibility of a SKYWARN spotter is to identify and describe severe local storms. In the average year, 10,000 severe thunderstorms, 5,000 floods and more than 1,000 tornadoes occur across the United States. These events threatened lives and property.
Since the program started in the 1970s, the information provided by SKYWARN spotters, coupled with Doppler radar technology, improved satellite and other data, has enabled NWS to issue more timely and accurate warnings for tornadoes, severe thunderstorms and flash floods.
SKYWARN storm spotters are part of the ranks of citizens who form the Nation's first line of defense against severe weather. There can be no finer reward than to know that their efforts have given communities the precious gift of time--seconds and minutes that can help save lives.
Part of your survival kit should be a radio which can receive the NOAA Weather Radio broadcasts. Although you can buy dedicated weather radios that strikes me as an inefficient use of your money. Rather, at a minimum get an AM/FM radio which can also receive the NWS broadcasts. Better yet, get some form of two-way radio with wide-band recieve which includes the ability to receive them. For example, the Midland CD Radio in my truck, and my Yaesu VX-5RS and FT-7800R ham radios can all receive the NWS channels. The Yaesus can also be setup to alert you if they receive a NOAA All Hazards Alert. If you're not a ham, some makers of FRS/GMRS radios offer models which incorporate weather radio reception.
Aside from listening to NOAA Weather Radio, you can also monitor SKYWARN radio nets conducted by volunteering hams. Local contact information for SKYWARN is available here, or a few minutes on Google will get you a link to information about your local net.
Edit 8/6/06: I updated the SKYWARN links above to more direct ones.