Public domain videos were either created for the public OR their copyright has ended. Many public domain videos are sold but you can get them free here. All videos can be used for personal (offline) projects for friends and family. Usually restrictions apply for businesses and published (online) projects like blogs. Read each web site's "copyright notice" or "user agreement" before using.
Internet Archive: Moving Images
Download public domain videos by category. When you locate a video you want the download links are on the FAR LEFT of your screen.
Library of Congress
"American Memory provides free and open access through the Internet to written and spoken words, sound recordings, still and moving images, prints, maps, and sheet music that document the American experience. It is a digital record of American history and creativity. These materials, from the collections of the Library of Congress and other institutions, chronicle historical events, people, places, and ideas that continue to shape America, serving the public as a resource for education and lifelong learning."
DOE - Nevada Historical Nuclear Weapons Test Films
"Pages on the DOE Nevada Web site are provided as a public service by the U.S. Department of Energy, Nevada Operations Office. Information presented on these pages are considered public information and may be distributed or copied. (Use of appropriate byline/photo/image credits is requested.)"
CREATIVE COMMONS
Vast resource for free video clips. Search for videos based on license-type and content available.