"The public domain is not a place. A work of authorship is in the 'public domain' if it is no longer under copyright protection or if it failed to meet the requirements for copyright protection. Works in the public domain may be used freely without the permission of the former copyright owner."
(U.S. Copyright Office Definitions, 2013; emphasis added)
As of 2013, works created before Dec 31, 1923 have all fallen into the public domain (PD). As copyright law has been amended several times in order to extend copyright protection (to the point that no American work will enter the PD until the 95-year limit hits works created since Jan 1, 1924, which will be on Jan 1, 2019) works can be designated Open Access, which allows for new works to enter the PD immediately, often through the use of Creative Commons licenses.
A thorough table of what is and is not in the public domain as of Jan 1 2013, from Cornell.
Works that are in the public domain are free to reuse and repurpose. These works enter the public domain once their term of copyright protection has expired; more recent works can also be designated for public use at their time of creation.
The information presented here is for informational purposes only and should not be considered legal advice.
These images want to be used and you should most definitely do so, but please cite the source institution. Though many of the public domain images are long out of copyright, citing the source institution (that is, the museum/library/etc. wherein the original image/material is held) makes it easier for others to track down the originals of the images you use. If you use any of these images in a paper, you must include a full citation of the image in your bibliography.