By going to the settings screen and clicking on 'Choose iPod Music', you can set your alarm to any song or sound in your iTunes.
Similarly, if you scroll down in the setting screen you can set what you fall asleep listening to by turning Ambient music from Off to On by tapping on the On/Off button and then pressing 'choose iPod music'. The default music can be used if you do not have any ambient music or sounds in your iTunes.