For me, YouTube on my Samsung Galaxy S3 is more of a music player, not a video player. I have tons of YouTube playlists for music, but since I'm mostly only interested in listening, it'd be nice if YouTube would continue to play in the background while I use other apps.
There are apps out there like NextVid that let you play YouTube videos in the background, but what if you actually want to see the video while you're browsing your Home screen or using other apps, not just listen to it?
For that, you have a few options. No root required.
Option #1: YouTube Floating Popup Player