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
NACIS and many volunteers support Natural Earth which is a "public domain map dataset ... featuring tightly integrated vector and raster data, with which you can make a variety of visually pleasing, well-crafted maps with GIS software."
NASA and CIESEN/Columbia University maintain the World Data Center which "provides access to a wide range of global data, associated documentation, and visualization and analysis tools, and to the community of experts on global data."
IPUMS-International "is an effort to inventory, preserve, harmonize, and disseminate census microdata from around the world. The project has collected the world's largest archive of publicly available census samples."
NASA and the University of Maryland maintain the Global Land Cover Facility which collects satellite data on land cover for the entire world.
Federal Government Internet Mapping Services
The Department of the Interior's Data.gov site is your one stop for federal, state and local geographic data, easy to search, browse and download.
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. Some web sites develop as part of specific policy initiatives, such as Data-Driven Detroit or The Greater New Orleans Community Data Center. 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. And here is a page of resources related to the Adirondack Mountains and the Adirondack Park.