The TIGER/Line Shapefiles are the core geographic product from the U.S. Census Bureau. They contain a vast quantity of data for the United States including detailed boundaries for administrative, political, and census areas.
This worldwide basemap dataset, available at three scales: 1:10 million, 1:50 million, and 1:110 million, is an excellent resource for making small-scale maps. It includes well attributed datasets for administrative boundaries (states and countries), disputed regions, and populated places.
OpenStreetMap is the worldwide, crowdsourced geographic database. It includes boundaries for places around the world, such as administrative areas, political divisions, protected areas, parks, and maritime limits.