Until about a month ago, I was using FireTube to play YouTube videos in the background while using other apps. But when YouTube discontinued version 2 of their API, this app stopped working. Presumably, the paid version did get updated to work with the latest version of YouTube, but I'd rather use a free product.
However, all the other apps I tried were either broken (many were still depending on the old API as well) or didn't truly play in the background; for example, some were displaying the video in an overlay over other open applications. This isn't acceptable for me because my phone doesn't have a large screen and I want to be able to use other applications without having to drag the overlay player around.
Unfortunately, it appears YouTube tries to get rid of this feature in apps; for example, on May 3 the Listen on Repeat did remove just the feature I am looking for because of pressure from YouTube.
I realize I can just download the MP3's using a service such as YouTube-MP3.org, but I've got little space on my SD card and downloading everything is quite inconvenient, so I'd rather use a streaming app.
TL;DR: I need an app that can stream music videos from YouTube unobtrusively in the background while I'm using other apps.