Natural Earth is a great site for a variety of natural and socio-political datasets such as rivers, roads, boundaries, on a global scale. Includes large scale sets (detailed) and small scale (generalized) data. Natural Earth data is optimized for cartography.
TIGER/line, produced by the U.S. Census, is the go-to source United States features such as state, country, or city level boundaries, roads, rivers, etc. Geodatabase format is recommended.
Cartographic Boundary Files, by the U.S. Census, are simplified versions of TIGER/Line files. These are ideal for small scale (i.e. zoomed out) mapping projects, not necessarily for analysis.
Boundary and administrative data with select US Census demographic data. Shapefiles have demographic data pre-joined; Geodatabases come with features (i.e. shapes) packaged with Census data tables. Caveat: table headings are not descriptive --you'll have to refer to a codebook to know which variables are which.
Free spatial data. International in scope. Here you can find administrative boundaries, transportation, and more. Much of Diva's data is based on public domain VMAP data.
(CU Boulder users only) Social Explorer contains downloadable U.S. Census data tables. The advantage of Social Explorer is its easy to use interface. Tables can be downloaded then joined to geospatial data.
Data-Planet is a great starting point for finding data. Many of the datasets available here can be exported pre-joined to shapefiles for use in GIS. Lots of economic and social data.
Contains U.S. population, housing, industry, and business data. Can be accessed by dataset or topic. Tables can be downloaded and joined to geospatial data. Basically the same data that can be found in Social Explorer.
Provides pre-2000 U.S. Census data (American FactFinder only contains the two most recent censuses plus ACS data). Aggregate census data and GIS-compatible boundary files for the United States between 1790 and 2013.
Users can download the national hydrography data using the data viewer (map interface) or by region or state. Data available in geodatabase or shapefile format.