If you have netflix, you really need to start trying out streaming. It's a really, really great feature and I can often find things to stream that are related to what the kids are learning. If you have a Wii or an internet connected blue ray player, you can even watch them on your TV instead of the computer.
I did try Blockbuster several years ago and wasn't a fan. The service wasn't very fast and the selection was a lot lower. They also won't carry any movies rated above R, and while that's not a problem when it comes to what the kids watch, sometimes I want to see an unrated director's cut of something, and that's not possible with Blockbuster. The plus was that, at the time, Blockbuster allowed you to change out your movies at a retail store rather than waiting to mail them. I'm not sure if they still do that, but even if they do, with so many of their retail stores closing, it would be a lot harder to use that benefit.