For all practical purposes, the public domain comprises copyright-free works: anyone can use them in any way and for whatever purpose. Proper attribution to the author or source of a work, even if it is in the public domain, is still required to avoid plagiarism.
The public domain is generally defined (e.g. by the U.S. Copyright Office) as the sum of works that are not copyrighted, i.e.
For the U.S., federal government works are not eligible for copyright protection (17 USC 105). It stands to reason that this applies world-wide, for it is not evident how the U.S. government could assert copyright in some other country over a work that cannot be copyrighted by its own laws in the originating country (the U.S.). Still, there are differing opinions, see the CENDI Copyright FAQ list, 3.1.7 and a discussion on that at the LibraryLaw Blog. For all practical purposes, however, we can assume works produced by the U.S. government or its employees in the course of their duties to be copyright-free and in the public domain world-wide.
In practice, this means that much material on *.gov and *.mil, as well as material on some *.us web sites (such as the sites of the U.S. Forest Service), are in the public domain. Please note that not all such material is in the public domain, though:
Under U.S. law, laws themselves and legal rulings also form a special class. All current or formerly binding laws, codes, and regulations produced by government at any level and the public record of any court case are in the public domain.  This applies even to the laws enacted in states and municipalities that ordinarily claim copyright over their work. The US Copyright Office has interpreted this as applying to all "edicts of government" both domestic and foreign.
Note that other countries' governments may hold copyrights; in fact, most do so and their works are thus copyright protected. At the same time, many countries declare their edicts such as laws and court decisions to be exempt from copyright. Such exemptions are typically narrowly defined and cannot be construed to mean "any publication by a government office".
The U.S. Copyright Office has clarified that works of the U.S. Postal Service, of the government of the District of Columbia, or of the government of Puerto Rico are not "works of the U.S. government" and thus are subject to copyright. Furthermore, works of the United Nations or its agencies or of the Organization of American States|OAS are subject to copyright. On the UN, see Works of the United Nations for some important exceptions: some UN documents are in the public domain.
A second category of works that in general cannot be copyright protected are those that have no (or no significant) creative content: they do not pass the threshold of originality. In the U.S., the classic example is a telephone directory. The names and numbers therein are, in the doctrine of case law, "facts that were discovered", rather than the result of a creative expression or judgment. The U.S. has explicitly rejected the position that the amount of effort involved in the discovery of a fact can justify its protection. As a result of this doctrine, addresses, phone numbers, most scientific data, sports scores, the results of polls, and similar facts are exempt from copyright.
While the facts themselves are exempt, other creative elements in a compilation of facts may warrant copyright protection. For example, Eckes v. Card Prices Update established that the specific selection of which facts to include in a list, when done as the result of a creative act, merits protection even when the individual elements do not. (See also 17 USC 103(b).) The WIPO Copyright Treaty is an international treaty that follows this concept; it has been adopted also by the European Union (EU) in its EU Database Directive, a sui generis protection that prohibits any significant "extraction" or "re-utilization" of information from a database created by significant effort. In all these cases, the copyright is on the database as a whole, i.e. the selection of the collection. The individual items in such databases still have their own copyright, which may have expired.
Similarly, though scientific data are usually exempt from copyright, the specific figures and styles of presentation used to present that data will in most cases merit copyright protection. Also, in some cases facts that are exempt from copyright may still be protected as a result of patent law.
Another class of uncreative works which are unable to claim copyright protection in the U.S. are those resulting from mechanical reproduction. Following Bridgeman Art Library v. Corel Corp., a simple reproductive photograph of a two-dimensional artwork does not give rise to a new copyright on the photograph. Many other countries (but not all!) recognize a similar ineligibility for copyright for reproductive photographs of two-dimensional public domain works.
Descriptions (including diagrams) in patent applications in the U.S. are "published into the public domain" by the U.S. Patent and Trademark Office . Portions may contain the non-obligatory notice of copyright © or mask work Ⓜ protection, but the patent applicant must state in the text of the description that the owner of the rights in the protected part agrees to allow anyone to make facsimile reproductions of those portions of the description, but otherwise reserves all rights 37 CFR § 1.71(e).
Photographic reproductions, as a form of derivative work, may inherit the copyright of the original work. If that artwork is in the public domain, then so is the photograph. If, however, the depicted work is copyright protected, then, although there is no independent copyright on the photo itself, it cannot be considered to be in the public domain as the original rights holder still has the authority to control how reproductions of his work, including photographs, are made and distributed. The same applies to digitized images.
It should also be noted that the exemption of reproduction photographs extends only to two-dimensional artwork in the U.S. A photograph of a three dimensional statue may acquire copyright protection even if the statue itself belongs to the public domain. Such rights derive from the creativity involved in the positioning of camera, lighting, and other variables.
In the U.S., the Compendium of Office Practices II of the U.S. Copyright Office gives some concrete examples and hints at under what conditions a work is sufficiently original to be eligible for copyright.
Public records are not necessarily in the public domain. Citizens generally have the right to access many items in the government's public records, but this right to access does not include a right to republish or redistribute the works so accessed. In general, copyright is neither lost nor waived when a work becomes part of the public record. Being in the public record and copyright are two orthogonal concepts. Uses of works from the public record must comply with copyright law.
Many items in the U.S. federal public records are in the public domain as works of the U.S. federal government, such as court decisions by federal courts, but the U.S. federal public records may also contain copyrighted works. This is even more so for public records of U.S. states.
For more information about original research, public domain, and appropriate sources, see Help:Contents. Adapted with thanks to Wikipedia