Eventually, copyrighted works pass into the public domain. Some works are in the public domain upon creation. Works in the public domain may be freely used for all purposes.
As a rule, anything created before 1926 is in the public domain. You may use it freely.
If the work was created after 1926, it may also be in the public domain. The rules depend on the date it was created, whether the author applied for a copyright extension, whether the author is still alive, and whether the work was made for hire or was made anonymously.
Anything created by the United States Government is in the public domain, so U.S. government websites are an excellent source for freely usable materials. However, it is important to ensure that the works used were created by the government and not on loan, purchased, etc. Examples of works created by the U.S. Government are WPA photography and US Geological Survey maps.
What is in the public domain today?
Adapted from Black’s Law Dictionary 9th ed.
When copyright, trademark, patent, or trade secret rights are lost or expire, the intellectual property they protected becomes part of the public domain and can be appropriated by anyone without liability for infringement.
A handy guide from Cornell University to determine if the work is currently under copyright or in the public domain.
The Copyright Office database includes all copyright registrations (including renewals) from 1978 onward.
The Stanford Copyright Renewal Database makes searchable the copyright renewal records received by the US Copyright Office between 1950 and 1992 for books published in the US between 1923 and 1963.
Google Books's Search of Scans of the Catalog of Copyright Entries provides full-text search of copyright registrations from 1922 to 1977.
How to investigate the copyright status of a work, from the U.S. Copyright Office (PDF)
American Library Association public domain digital slider
Chart describing when works pass into the public domain, from UNC Chapel Hill Libraries