Speeches on the floor of the House and Senate are published in the Congressional Record, published daily when Congress is in session. The Congressional Record provides a full record of the proceedings of both the House and the Senate, and is organized in four parts:
The Extensions of Remarks includes text that was not part of floor activity, but was inserted later; the Daily Digest is a summary of all Congressional activity for that day.
There are two editions of the Congressional Record: the daily edition and the bound (permanent) edition. The bound edition is produced following each session of Congress, when the daily Congressional Record is revised, printed, and bound. (The bound edition is also available in electronic format.)
What is the Congressional Record? (published by ProQuest) is an excellent, brief introduction; well worth reading for anyone planning to do research using the Record.
The Congressional Record began publication in 1873. Prior to that, Congressional debates were published in The Debates and Proceedings in the Congress of the United States (also known as the Annals of Congress, 1789-1824), The Register of Debates in Congress (1824-1837), and The Congressional Globe (1833-1873).
The Congressional Record's predecessors are not identical to the Record; most include summaries, not verbatim transcripts of debates, and some volumes (like the Annals) were not published contemporaneously, but compiled later from sources like newspaper accounts.
In addition to the sources below, the Congressional Record's predecessors can also be found in ProQuest Congressional and HeinOnline, two of Yale's subscription databases. See "Finding the Congressional Record" above for more information.