Many newer TV sets have the ability to play video files from a USB hard drive. Getting movies onto the drive is the major challenge. DVDs can be ripped using a computer. The problem with this is that almost all DVDs are copy protected. There are ways to circumvent this and the consensus is that it's legal to do for DVDs that you own.
If you have access to services like Hulu, Netflix or Amazon Prime you can stream movies and TV shows to a computer, TV, or devices like Roku or DVD/Bluray players. The problem though is that this does not get saved for viewing later. Here's an article from PCWorld discussing ways to save streaming video:
How to download streaming media and watch it anywhere, anytime