Earthquakes: The United States Geological Survey's (USGS) earthquake page has a constantly updating webpage on earth tremors felt around the world. Each page has information ranging from how strong a quake was to p-wave data to maps. Check out the Chilean earthquake's page for a good example.
Tsunamis: The National Weather Service has the excellent Pacific Tsunami Warning Center which despite the name covers tsunamis around the world.
Extreme Weather: The National Weather Service wins this one as well for extreme weather in the United States.
Volcanoes: USGS has a Google Maps mashup showing American volcanoes and their status along with any warnings.
Fires: This one is not as developed yet. Local news agencies seem to be the best place to go for specific fires. However, FIRMS by the University of Maryland is the best place to go for worldwide fire mapping. They also have GIS shapefiles on fire data.
Disasters that Cause Population Displacement: Hands down this goes to Relief Web. The Haiti page, for example. has enough maps to answer any internally displaced person/relief organization question you may have concerning the January 2010 earthquake.
Also, be sure to check out and subscribe to Geographic Travels' Twitter feed. When major geographical events are taking place I will be updating here as I get information.