There's online rental which is really the direct replacement for rental stores... I would say most stuff is on there.
iTunes store, and Google Play store both have buy/rent options that are on a per movie basis. Unlike Netflix where you pay per month and get access to all their content. I believe Amazon also has a service like this, which I hear is good, but I think you need to have a free registration with Amazon Prime first? Not really sure...
Some stuff you can buy, and some content you can rent or buy...