The House Rules Committee hosts an indispensable site that gathers together the Congressional Research service reports on the legislative process. This is the collection of information about the nuts and bolts of legislation.
Digitized and searchable facsimiles of early congressional documents is available at the Century of Lawmaking for a New Nation site. Totally cool! You can also search the House and Senate Journals up to the 42nd Congress (up to 1873), in addition to other documents.
The Center for Legislative Archives of the National Archives and Records Administration keeps old original congressional records that you can travel to DC to do research on. This site is also useful for doing research far away from DC.
C-SPAN to see live television from the floor of the House and Senate.
The Dirksen Center has created a site called Congress Link, which contains a mixture of good congressional links and academic exercises.
A research project at UNC-Chapel Hill is trying to develop a user-friendly filter for searching the Congressional Record.
The Campaign Finance Institute site is very useful, particularly in providing an on-line version of the campaign finance tables that are published in Vital Statistics on Congress, 2001-2002. (Vital Statistics is an indispensable reference source for any student of American politics.
FEC Info is a private Web site that turns around FEC data. This is sometimes more useful than the FEC site.
The Center for Responsive Politics has a lot of information about individual MCs, particularly information about campaign finance.
The Washington Post has a very good page that points to U.S. Government information sites, including Congress.
The Dirksen Center honors the memory of Sen. Everett M. Dirksen. It has grants and educational programs that are of some interest to the professional and student, alike. Their Congress Link page has a lot of resources that are helpful to teachers and students of Congress.
Congressional Observer Publications has a bunch of information (including roll call votes) about Congress. This is a commercial site, but it looks good.
While it's not data - it's software - the PoliSim election simulator provides a pretty neat visualization of how spatial models of electoral competition work. (The page is now about 8 years old and written in Java® 1.0. Please take the fellow up on his challenge to update it.)
The Legislative Studies Section of the American Political Science Association has its own home page, including the electronic version of its newsletter and other legislative links.
Pollingreport.com has the most comprehensive set of reports about recent public opinion polls.
Here are some links to sources for news about Congress.