Below, we have listed several sites with videos that you may be able to use in your projects without getting permission from the copyright holder. Be sure to check the copyright/license status and be sure it matches with your use - it is your responsibility to determine that your use of third-party materials is legal!
YouTube is platform that allows users to watch videos that have been uploaded and shared by other users. There is a very broad range of videos which are created not only by individuals but also by organizations and corporations. When you get your search results, set the filter to Creative Commons to limit your results to CC-licensed videos.
Vimeo is another platform that allows users to watch videos that have been uploaded and shared by others. When you get your search results, under Refine results by, select +More Filters, then License, to limit your results to CC-licensed videos. Vimeo also has pages where you can browse all of their Creative Commons licensed videos or public domain videos.
Wikimedia Commons is a media file repository making available public domain and freely-licensed media content. Wikimedia Commons has a page where you can browse all of their Creative Commons licensed videos.
This library contains digital movies uploaded by Archive users which range from classic full-length films, to daily alternative news broadcasts, to cartoons and concerts. Many of these videos are available for free download.
This archive collects, preserves, and provides access to films of historic significance that haven't been collected elsewhere. Included are films produced by and for many US corporations, nonprofit organizations, trade associations, community and interest groups, and educational institutions, as well as home movies and amateur films. Many films from this archive are in the public domain.
Most films and video produced by federal government agencies are also in the public domain and can be used freely.
TED has a collection of short (18 minutes or less) videos from "inspired thinkers." Non-profit organizations are encouraged to share TED Talks through social media and to embed individual talks in contextually relevant ways on non-commercial websites. The site has a detailed usage policy.