First, the bad news. Streaming services that use a monthly fee are not supported. They use their own apps which use DRM (Digital Rights Management) to decrypt and play videos downloaded from their services. This includes iTunes, XBox Video, Amazon, NetFlix, and many others.
The good news
But there are other options. The easiest with the best selection is YouTube. There are several Apps in every App Store for all device types, many of them are free. To find one, just search for "YouTube Downloader" using the operating system's built-in App store.
Our app itself does not support downloading videos, however let us know in the feedback page within the app or any one of our social networking pages if you find a favorite.