When disaster stikes, a variety of emergency response and relief agencies respond - along with the media. The web is an excellent resource for current information on disaster response and recovery. One of the best sources for information on disasters in progress is the National Weather Service National Warnings site which lists all current watches (an event has the possibility of occurring) and warnings (an event is imminent or is occurring) for the entire United States. Once disaster stikes, it's just a matter of locating news about the event from such places as CNN or The Nando Times. California, noted for its frequent tremors, benefits from the state's Office of Emergency Services which maintains a gopher site known as EDIS (Emergency Digital Information Service) which is a direct feed of emergency information from California's state and local governments. If you live in the Bay Area you'll want know how much shaking you can expect when the "Next One" strikes.
For summaries of relief information, I stongly encourage a visit to Disaster Relief, containing reports from disasters worldwide, emphasizing information from the Red Cross. The U.S. Federal Emergency Management Agency posts updates on disasters and contains a plethora of information to help you prepare for disaster. For worldwide humanitarian and disaster relief, I recommend the United Nation's ReliefWeb.
Feeling overwhelmed trying to keep up with disasters around the world? Earthweek provides a weekly synopsis of natural disaster and interesting natural events occuring on our planet. For the disaster fan, it's a must-see.