The US government's 'Topologically Integrated Geographic Encoding and Referencing' system, usually referred to as TIGER, is based on an extensive database of US geographic information. It is county-level data that documents physical features like roads and rivers, as well as some administrative features such as Congressional districts. Data can be downloaded for each state and for each of the following: Puerto Rico, American Samoa, Guam, Northern Mariana Islands, Midway Island, and the US Virgin Islands.
The database does not contain demographic or topographic (terrain) data; the "topology" referenced in the name refers to how the database itself is designed.
Only recent versions are available online for free download. Note also that the Census Bureau is making substantial changes to how the TIGER system is formatted, which should allow for wider and more effective compatibility with GIS tools. A good overview can be seen at this page