How to remove cloud songs from Music app? During Christmas 2013, Apple an official app that gave out free downloads for a week or so. I used that app to get some free songs. Now they appear forever stuck in my Music app. I don't want to see them. Swiping left on the song didn't do anything. Also, I didn't see how to manage these songs in iTunes on my computer.
Launch the Settings app then go to "Music" and toggle the "Show All Music" switch to "Only music that has been downloaded to this device will be shown."

This same feature is available for the Video app.