YouTube is the largest and most popular video streaming site by far. It's also a good place to listen to popular music, including current hits.  YouTube is also rife with homemade shows and series of all kinds. These usually have low production value but can be quite entertaining and informative. Movies and mainstream TV shows can be found on YouTube, but more popular and well-known properties usually get taken off the site for copyright reasons. There are, however, a whole lot of movies in the public domain (not under copyright anymore). Hulu is a mainstream video site like YouTube that bridges the gap between free content and professional content. It features a rotating menu of films and TV shows for free, plus a more expansive monthly pay service.  Hulu tends to have a lot of free TV shows, but very few A-list shows. There's usually a mix of older and newer shows available. Hulu's free film selection is fairly small, but it's easy to search. Again, expect a mix of old and new titles. This site is a direct competitor to YouTube. As with YouTube, all of Vimeo's content is free, but users can pay a fee to upgrade to higher-quality streaming and more space to upload their own videos.  Vimeo features independent, professional-quality work, such as artistic short films, as a point of pride. It also features plenty of ordinary user-created content. TV shows and wide-release movies are rare on Vimeo, but obscure and small-budget projects abound.

Summary:
Start with YouTube. Check out hulu.com. Spend some time at vimeo.com.