An Internet Mapping Service allows government and other agencies to provide access to maps and other data through a web site. This information can be viewed online or often downloaded as data layers for other maps.
National and International Internet Mapping Services
ESRI's ArcGISOnline provides access to many types of geographic content world-wide, including dynamic maps, interest groups, and more advanced Web services. One can also access a web-based version of ArcExplorer here.
The USGS provides national and international resources in the Seamless Data Distribution System.
Federal Government Internet Mapping Services
The Department of the Interior's Geospatial One-Stop Portal is your one stop for federal, state and local geographic data, featuring the National Map.
Access census data easily via American Factfinder, provided by the Census Bureau. The "Using FactFinder" page offers a very clear explanation of census geography and a tutorial on creating and using maps.
Create and print your own map at The National Atlas -- billed as "the single best Federal source for national maps and geographic information on the Web."
The USGS manages the National Map -- "the nation's topographic map for the 21st century."
State and Metropolitan Internet Mapping Services
Almost every state and large metropolitan area now has an internet mapping service to provide public access to geospatial data collected at the taxpayers' expense. Your best approach is to search (for example, using Google or other search engine of your choice) for the phrase "GIS" and whatever state or locality you are interested in.
For example, a search for "GIS and Chicago" will result in (among others) the City of Chicago GIS page. If you perform the same search with the search terms "GIS and Boston," you will discover that all Boston information is simply part of Massachusetts GIS, a state agency (though you might also want to check out the blog Bostonography). Some state departments might have their own services, such as the NYS DEC Mapping Gateway. As a final example, here is an entire page of IMS sites found by looking for information on New York City and GIS.
Thematically-Related Internet Mapping Services
One may also find a wealth of information by looking for mapping resources related to a particular event or theme. For example, here is a page of resources on Hurricane Katrina and Other Natural Disasters.