For moving images, there is YouTube of course, which carries a vast range of materials.
Advertolog is an online collection of recent adverts, divided into print/outdoor and tv/film/digital. You can search by brand, product and advertising agency. Ads of the World does a similar job, though is a bit less user-friendly, I found. Campaign is the advertising profession's magazine in the UK. It carries both discussion of adverts, and a collection of all sorts of advertising too. For collections of recent television advertisements, try the Creative Lounge, which is hosted by the UK newspaper The Guardian and has mainly ads broadcast in the UK. All the entrants to the British Television Advertising Awards since 1977 can be found in the Arrows archive. YouTube also carries a lot of video and film advertisements, of course.
The BBC Motion Gallery links to a range of film archives, including CBS and the Smithsonian. Public information films made by the UK government between 1945 and 2006 can now be seen online at the National Archives.
British films and television programmes are available at BFI Screen Online. In the US, Hulu is the place to find recent television and some films.
The Pathe archive carries newsreel, sports footage, social history documentaries, entertainment and music stories from 1896 to 1976.
Movieclips has a huge range of clips from movies (though the whole movie should also be watched), and there is also a site for film trailers.
The UK's National Media Museum has extensive collections of images and objects relating to television, film, photography and new media.