Android: Few apps are less kind to your limited data plan than YouTube. If you want to download videos to watch offline, you can subscribe to YouTube Red or use the new, free YouTube Go.
YouTube Go is a new project from Google aimed at developing countries. It's designed to use the absolute minimum amount of data possible. The app shows you a preview of the video you're about to watch before giving you a choice to download it in either "basic" or "standard" quality.
Neither of those options will look amazing or anything. In fact, you can't even get 720p video from the app. However, if you're trying to save as much data as possible, this gives you a ton of breathing room. Best of all, those videos will still be there even if you lose your internet connection. Technically YouTube Go is listed as "unreleased" but you can try it out now.
YouTube Go [Google Play Store]