Maybe you have some videos on your YouTube channel which you would like to save to your Android device, to show to friends or family, or even watch when you don't have an internet connection.
TubeMate is a great app which enables you to download YouTube videos straight to your Android device. You can download multiple videos at once, leave them downloading in the background or even pause them, and download later. You can convert select videos to plain MP3 if you wish. It also supports downloading videos at full HD 1080p.
It's free but unfortunately it isn't available on the Android market. I don't know exactly why because it was on the market at one point.
You will have to download the APK, load it on to your SD card and install manually which is easy to do.