Internet Archive is a digital library that provides access to thousands of free videos in the public domain. This is a great resource for silent films and many older foreign films which are now out of copyright.
UbuWeb is a repository for Avant-Gard and other experimental film. Popular films include Robert Smithson's Spiral Jetty. Please Note: UbuWeb openly defies copyright law and posts most if not all of their videos without the permission of the copyright holder, so use this resource with caution.
The National Film Board of Canada has an "online screening room" where they provide free access to many Canadian-made films, including animated titles, documentaries, and short dramas in addition to some new releases. Here, you can find many of Norman McLaren's films including his Oscar-winning short "Neighbours", as well a other popular films like "Buster Keaton Rides Again".
Many films in the public domain, silent films, and open access videos can be found on Youtube, as well as documentaries which have been made available for free. Netflix has made Ava DuVernay's 13th available, and PBS has placed many of its American Experience films on a Youtube Channel. The Youtube Movies channel also has many films available free with ads.
Youtube channels managed by the federal government, including NASA, USGS, and NOAA are not subject to copyright. These channels have open access videos including space exploration footage, volcano and earthquake footage, and underwater footage. Please note: this applies only to official federal accounts, and does not include state or local agencies which may still be subject to copyright.
In addition, you can easily search for films licensed through Creative Commons, which can be used openly for a variety of purposes so long as the original creator is credited. You can learn more about Creative Commons on Youtube on their FAQ page. See the video below for more information on finding Creative Commons- licensed videos on Youtube.