Al Jazeera maintains a repository of their videos under a CC BY license.
C-Span permits use of their video for historical, educational, research, and archival purposes. Individuals are permitted to post their video coverage of federal government events on a non-commercial public internet site with attribution.
USA.gov has a portal to the video collections of US government agencies, most of which are in the public domain and are free of restrictions for non-commercial use except for attribution. There are some exceptions, however, so check the terms of each agency.
The WikiMedia Commons maintains a search page for videos. All media on the site falls under one or another Creative Commons licenses, or are in the public domain.
Videezy is a subset of the image search site Compfight. It features free HD stock video footage which can be freely used for personal video projects.
The Miller Nichols Library also maintains subscriptions to several streaming media services, which cover permissions for streaming music or film for classroom purposes.