OGYouTube is a very unique YouTube client that lets you download any video from YouTube directly to the memory of your Android device. Best of all, you can do it in any of the available resolutions, and even directly in MP3 format.
In general, OGYouTube works exactly like the official YouTube client. Actually, it's an older version of the official client, with just one small difference: a download button below each video. Pressing this button lets you choose the format and quality of the video you want to download to your device's memory.
Naturally, with OGYouTube you can do that you can with the official YouTube client, like playing videos in the background. That said, it is VERY IMPORTANT that you don't log in with your account on OGYouTube. If you do, you won't be able to download videos anymore. For this reason, it's very important not to log in.
OGYouTube is probably the best YouTube download client you can find on Android, even if there are others that are also very good. Its usability and interface (the same as YouTube) make it the best possible alternative for downloading videos.