Internet archive has both moving images and stills including public
domain; others are licensed under creative commons (CC).
http://www.internetarchive.org

and here are the various searches by CC license type:
http://is.gd/dMHCl

Also searching flickr by CC license
http://www.flickr.com/search/advanced/?
flickr does have some very short film clips.

I’m sure there are other tools, even the creativecommons website has
searching functionality.

Youtube allows searching by license, too.

Also, fair use may come into play depending on what the footage is to be
used for.