First, a few general sites to use in any search for disaster-related resources, and then examples of what you might come up with if you searched for a particular event and GIS. Most of the following sites will have resources for multiple events; these are examples to give you ideas, not exhaustive listings.
ESRI provides a Disaster Response web site for information on all types of disasters -- wildfires, earthquakes, flooding, etc. This includes continuously-updated map viewers and extensive resource pages.
Google's Crisis Response project works with government agencies, NGOs and other organizations to provide information in the case of natural disasters and to assist with emergency responses (the latter page includes case studies).
Crisis Commons "seeks to advance and support the use of open data and volunteer technology communities to catalyze innovation in crisis management and global development." They sponsor crisis camps and wikis to enable volunteers to assist in disaster response.
You can expect that any large natural event such as a hurricane or earthquake will be covered by relevant government agencies such as NOAA, FEMA, NASA, USGS, etc. Major newspapers are also often a good source of news and interactive media; bloggers can also provide lists of resources.
Infoplease can be a useful starting point for general information about disasters, natural and man-made.
Not originally focused on hurricanes, the Greater New Orleans Community Data Center now includes updates for Katrina in addition to their extensive collection of mapped census data.
The Times-Picayune has a detailed animation of the hour-by-hour Flooding of New Orleans (you will need Flash on your computer to view this).
Find news, maps and images in the Hurricane Digital Memory Bank.
The Perry-Castañeda Library Map Collection (UT/Austin) has developed an extensive clearinghouse of Katrina related images and maps.
The New York Times's own interactive multimedia on the Impact of Hurricane Katrina features several maps prepared with GIS.
Washington University in St Louis developed an interesting damage assessment tool using satellite imagery to illustrate the extent of the disaster. This site includes the address of web services which can be incorporated into other sites or mapping tools as well.
Japan Quake Map shows an amazing time-lapse sequence of earthquakes beginning on March 11, 2011, which really gives a sense of the aftershocks.
The GIS Doctor provided an initial listing of GIS resources related to the quake.
Google's Crisis Response project maintains a page on the Gulf of Mexico 2010 Oil Spill, which includes a multi-layered map, KML files for Google Earth, an index of map and data sites, news and help resources, and a playlist of videos of the spill.
Independent researchers often develop useful tools, such as How Big is the Gulf Oil Spill?.
Gulf County, Florida has a nice page of GIS resources.