Why is my iTunes Music app suddenly skipping every track?
Solution 1:
It was reported earlier today on multiple sources that Apple services were experiencing outages throughout the day. Service seems to have been restored after about an hour or so of outage, and Apple has yet to officially respond as the reasons why but it did correspond during the VMA announcement.
For future status of their online services don't forget to check - https://www.apple.com/support/systemstatus/
Solution 2:
I had the same issue today. Reading through various threads a common theme kept coming up. Log out/in from iTunes. I went into Settings on my iPhone 6+ then clicked on my Apple ID at the top. Then I clicked Sign Out. Then I logged back in. When I went back to the Music app, I shuffled my songs and they all played which is a mix of iTunes Match music and Purchased music. (I don't subscribe to Apple Music. I don't trust it. After all these years of carefully perfecting my library the last thing I need is it getting hosed.) Anyway, give it a try. It worked for me.