Currently, there are over 400 departments, agencies, and sub-agencies in the federal government. A full list of U.S. government agencies and departments is available here. Many of these offices provide excellent internships for students looking to learn the ins and outs of federal bureaucracy. A great place to look for internships in any of the federal agencies is USAjobs.gov or on this page that details internship opportunities across a number of agencies. In addition, below are some of the agencies to which students often wish to apply.
Department of Health and Human Services
Consumer Financial Protection Bureau
National Geospatial-Intelligence Agency
Public Defender Service for the District of Columbia
Department of Housing and Urban Development