Copyright is a "limited" monopoly -- after a specified period of time, copyright expires and the work enters the public domain. If a work has entered the public domain, it can be used without looking for exceptions, invoking Fair Use, or asking for permission -- although it must be properly cited in order to avoid plagiarism.
Works published in the United States prior to 1927 have entered the public domain. Beyond that clear, bright line, determining whether a work has entered the public domain can be challenging.
In addition, most US government documents are in the public domain, excluding some US government documents that were created by contractors (not US government employees). State government documents may or may not be in the public domain; likewise government documents produced in other countries may or may not be in the public domain.
The following resources can help determine if a work could be in the public domain:
Under current US law, the creator of a work owns the copyright of that work automatically, without registering the work or providing notice (©). However, through the process of publishing a work, the creator may transfer all or some of the copyright to another entity -- a journal or book publisher, for example. Additionally, there are a variety of permutations on how rights can be transferred:
Copyright transfers must be written, signed documents. Consequently, it is very important to read publisher agreements before signing them so that you understand what rights you are transferring to the publisher and whether or not those rights are being transferred exclusively or non-exclusively. Also keep the signed publisher agreements where you can find them. The rights you have retained in those signed agreements will determine how you can use your work in the future. If you need assistance in interpreting a publisher's agreement, contact firstname.lastname@example.org.
A word about pre-prints (journal articles before the peer review process) and post-prints (journal articles after changes have been made as a result of the peer review process) -- many journal publishers allow creators to place their pre-prints or post-prints in openly accessible repositories (like BEARdocs) or on web pages. The SHERPA/RoMEO database helps scholars determine copyright and self-archiving policies for a wide variety of publishers.