Posting of short excerpts of copyrighted works on YouTube in our view constitutes fair use and is permissible under copyright law. YouTube has a process by which copyright holders can ask that a posted video clip be removed; this is discussed in:
http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2008/08/20/MNU412FKRL.DTL
YouTube is a subsidiary of Google, a large, reputable company. Our default assumption is that any video clip on YouTube has been posted with the tacit (at least) approval of the copyright holder and may be legally viewed.