You'll need a third party app to save and play songs without using iTunes.
Once you have a compatible app, tap and hold on the mp3 in Mail to get the popup menu. If iOS 6, you will see several options, including icons of compatible apps. If iOS 5 you will see an Open In option, and then a list of compatible apps.
I use OPlayer for this. It's popular, but there are several other good audio and video player apps to chose from.
You can't save to the Music app from Mail. The only way to copy songs to the Music app is through iTunes or a third party music manager for your computer. There are a few, but I don't remember their names.