United States Congressional Serial Set (now available online in Congressional Publications link above)
As described by the Library of Congress, "The Serial Set contains the House and Senate Documents and the House and Senate Reports. The reports are usually from congressional committees dealing with proposed legislation and issues under investigation. The documents include all other papers... printed by the House or Senate. Documents cover a wide variety of topics and may include reports of executive departments and independent organizations, reports of special investigations made for Congress, and annual reports of non-governmental organizations.
Congressional Record 1873- to Date
Provides for a full, although unofficial record of the proceedings of Congress, it has been published by the government since 1873 to date.
Congressional Globe 1833 - 1873
This predates the Congressional Record, it contains the record of Congressional debates of the 23rd through 42nd Congresses (1833-73).
Register of Debates of Congress, 1824 - 1837
Debates and Proceedings in the Congress of the United States (or Annals of Congress), 1789-1824
Predates the Congressional Globe. As described by Library of Congress "the Annals were not published contemporaneously, but were compiled between 1834 and 1856, using the best records available, primarily newspaper accounts. Speeches are paraphrased rather than presented verbatim, but the record of debate is nonetheless fuller than that available from the House and Senate Journals."
U.S. Statutes at Large
Contains every public and private law passed by Congress, executive orders, proclamations, in order enacted. Available for the following years:
Senate Journals, House Journals & Other Online Congressional Documents 1774 - 1875
Foreign Relations of the United States
'Foreign Relations of the United States series is the official documentary historical record of major U.S. foreign policy decisions that have been declassified and edited for publication. The series is produced by the State Department's Office of the Historian and printed volumes are available from the Government Printing Office."
Public Papers of the Presidents