Turner Classic Movies is now posting feature film length videos on their MediaRoom website. Up until recently, you could only watch trailers, shorts and promos in the form of short video clips. Now, they are posting entire films! Mostly obscure ones not available on DVD. The quality is good and the video screen is larger than your normal online video clip would be. I highly recommend watching one. I recently saw Living On Love (1937) on the website and was very happy with the experience. Here is their current selection.
Living On Love (1937)
Way Out West (1937)
One Million, B.C. (1940)
Go Johnny Go! (1959)
If you don't mind really tiny, poor-quality video screens, then you can also try Internet Archive's Moving Images library. I love this website, mostly because I can find my old music page on there from back in the day in their Wayback Machine, but also because you can find feature-length films as well as old shorts in the Moving Images section. So, what are you waiting for? Check it out!