PodTube allows you to easily download videos from Youtube and save them into your smartphone.
You can add your favorite channels and PodTube will automatically download latest videos from them, allowing you to view or listen to them offline as podcasts in your favorite player.
If you want, you can also only download the sound track (instead of the full video), which will save you a ton of space and data charges, if you only want to listen to the audio and don't really need the video.