See also: Wikipedia:Videos
As an open content encyclopedia and a poor not-for-profit, we simply don't have the money to pay to license video streaming servers or codecs, and with proprietary codecs we have no assurance that we won't have to at some stage. Furthermore, using patent encumbered codecs violates the "free access" tenet on which Wikimedia projects are based.
Using free codecs, the cost of the software to the Wikimedia Foundation to serve video is zero. The cost of the disk storage to store it and the bandwidth to serve it up is not zero.
Video should not be uploaded simply for the sake of uploading video; it should convey something which cannot be conveyed via pictures or text. w:Wikipedia:Videos#Types_of_videos lists some examples of where video is appropriate.
We should set a maximum resolution guideline, so as to balance the desirability of having high-quality content with the high costs of storing and serving DVD-quality video.
Serving from offsite
It would also be good to explore options for having videos served from outside wikimedia to reduce bandwidth costs. One obvious option is to store files on wikimedia's servers, but have the actual video playback handled by user-contributed mirror servers, youtube, or some other option.
WebM and Ogg formats are playable in all modern browsers. It is important that video be available in lower resolutions to serve people with lower bandwidth connections; currently the UploadWizard automatically downsamples high-resolution videos to lower resolutions to serve this need.
Obviously, copyright law applies to video as it does to text and images, and privacy laws also apply in some cases — again, the same as with still images. IANAL. Some further guidance as to fair use of copyrighted video is required.
One additional issue might be if people start uploading sexually explicit material. There may be laws in the United States beyond copyright laws that pose very specific consent requirements regarding this sort of thing, and investing time in ensuring compliance with these laws is likely not the best use of Wikipedia's time. Probably the best thing to do is simply impose a moratorium on such clips.
Priorities for video coverage
We are of course dictated by what is already available in the public domain (e.g. a lot of material at archive.org), and what interests people enough to point a camera.
However, in terms of encouragement towards (or selection of where we have limited resources) subjects where video is particularly helpful in illustration (for instance, sports or hobbies), and where there isn't lots of other material readily available. I'm not convinced movie trailers, for instance, are a good use of Wikipedia resources.
Because of video's costs, we should be prepared to discard video that doesn't add something that an image or unaccompanied audio wouldn't.
See http://wikimania.wikimedia.org/wiki/Competitions for the Wikimania media contest.