Is there an app that allows me to set music as an alarm? Let me preface this by saying that I am not looking to set music in the built-in iOS Clock app. I have tried that and I had problems with it. I usually keep all sounds muted, so it won't work. I also tried Alarm Clock HD, which plays music as an alarm but it won't work for me as I needed to be running in the background. I am also using an iPod touch, so bmike's suggestion isn't feasible.
Here's what I'm looking for: an app that will allow me to a set a song for an alarm and will play that song even if the app is in the background. Alarm Clock HD also had a nice volume feature, which automatically turned up the volume all the way (which is really nice). Is there an iOS app that will do this?
As of iOS 8, the native Clock app supports selecting your own music. When selecting a sound, choose "Pick a song" at the top. Presto!