There are a number of archives where you might consider depositing your films and videos. However, you are already aware that film and video are fragile and that archives, like most nonprofit organizations, often have financial difficulties. These are all reasons to start the process of placing your work early.
The general advice that applies to other disciplines is true for film and video. Try to find a person who has a working knowledge of the field to make responsible for your work. Having the time to discuss your wishes with this person and to create a plan to implement those wishes is vital.
ArchivesYou will need to consult with the archive staff to determine which institution your work would be most appropriate for. Some archives may primarily store their materials, others may also exhibit and distribute work. Because of financial conditions, few archives can provide full conservation services.
You should also look carefully at the conditions under which work is stored. Film is a particularly fragile medium. While video is somewhat more stable, controlled storage conditions are still important for its long-term survival.
It is always helpful if you can provide an archive with both the master print or tape (which should not be played or projected) and a quality print. If your materials are organized and labeled, it will make it easier for an archive to effectively use them. It will also make clear your intentions for use of the material. You may have other materials, such as out-takes or scripts, that you feel are important to preserve along with your work but these are exactly the type of materials that are important to organize effectively. An archive will be unlikely to have the staff and resources to sort through extensive materials determining which are of importance.
Like visual artists, you especially need planning time. Until the film and video community, as a whole, finds additional resources for preservation, careful planning is one of the best tools you have to ensure the survival of your work.