The Weather Channel Web Site: Very useful, and customizable to your own city!
MSNBC's Intellicast Weather: My favorite part of the site--the local doppler radar images--updated every half hour!
CNN's Weather Center: Plenty of maps and information from CNN.
Accuweather: Weather provider for many sources. Try signing up for "personal accuweather" a free, VERY detailed local forecast, through them.
The Weather Underground: My personal favorite for looking at current conditions and watches or warnings around your home state.
Weatherspout: Source of many excellent current MPEG weather movies.
Earthwatch: Excellent source for storm weather.