Self-described as a service for movie lovers, the main emphasis of Fandor is on independent and foreign movies. This includes a wide range of various films, but it includes a large library of classics. This service works with libraries and universities throughout the US to provide streaming movies for members.
If you have a library card, you need to be using Kanopy. If you're a fan of shorts from this time period, the Prelinger Archives are hosted here as well, with various educational and promotional short films to keep you busy for hours on end. This includes a vast selection of public domain films. You may know at the home of the Wayback Machine, but as the name says, it's an archive of various sorts of digital media. Some of the movies you'll find are newer than what I think of when I think of classics, but you may view this as a plus. One of the easiest ways is to hop on to your computer and point your browser to the website, then select Classics from the genre selector. Depending on how you access the service, they can be difficult to find. While the selection isn't what it used to be, you can still find some classic movies on Netflix.