Here's the beginning of a list of data and APIs available related to the workings of the U.S. government.
Other Data Catalogs
CKAN: "us" tag - United States related data at the Comprehensive Knowledge Archive Network.
USGovXML is an index of publically available web services and XML data sources that are provided by the US government.
Legislative Data (bills, votes, members of congress)
Capitol Words API: Word popularity analysis on the daily congressional record and provides a list of the most popular words in congress on a day by day basis. With the Capitol Words API you can see trends of word use in congress.
GovTrack Data and APIs: Database and APIs for U.S. federal legislation, Members of Congress, voting records, etc. Also an API for looking up congressional districts by address, lat-long, and ZIP+4, and a downloadble ZIP+4-to-congressional-district database.
MetaVid: Video of the U.S. House and Senate floor.
New York Times API: New York State legislature membership and committees, U.S. Congress votes, and campaign finance data for presidential elections.
Sunlight Labs API: Basic information on Members of Congress, legislator IDs used by various websites, and lookups between places and the politicians that represent them. The primary purpose of the API is to facilitate mashups involving politicians and the various other APIs that are out there.
Vote-Smart API provides biographical information and legislative information, such as key vote summaries, for Congress and state governments. Also information on members of the executive branch of the federal and state governments.
WatchDog.net Database of congressional information.
Federal Budget and Spending
USASpending.gov Data and APIs for federal grants and contracts.
EarmarkWatch.org, Taxpayers for common Sense, and Earmarks.OMB.gov: Earmarks in federal legislation.
Campaign Finance, Lobbying, and Financial Disclosures
FollowTheMoney API for campaign contribution and financial data for state politicians.
New York Times API: New York State legislature membership and committees, U.S. Congress votes, and campaign finance data for presidential elections.
OpenSecrets API for campaign contributions and financial data for Members of Congress.
Legal Documents and Judicial Data
United States Code: See the Cornell LII and the Library of Congress US Code page.
bulk.resource.org/courts.gov: 710,000 federal appeals cases in XHTML
pacer.resource.org: 735 GB of district court cases from PACER
AltLaw.org: ~100,000 cases downloaded from appeals court web sites
USCourts.gov: Many court web sites archive opinions from the last 10-15 years
Geospatial
Cicero: Address-based, District Matching and Elected Official Lookup Web API - Web-based API that takes any address in the United States and finds and maps the matching legislative districts as well as information on the local, state, and national elected officials who represent the address.
Mobile Commons Legislative Lookup API to map latitude-longitude coordinates to federal (Congress) and state legislative districts.
A list of each state border and its length - Helpful when considering interstate commerce legislation
CAVoterConnect KML data for California state jurisdictions including congressional districts in KML format.