If you need some background noise to aid your sleep, White Noise for iPad or iPhone has a wide selection available, from ocean waves crashing to crickets chirping to frogs croaking to a shower running. You can also use the app's Mix Pad to make your own sounds (some are preset) and add them on top of music playing from your stored library. Once you choose your background sound, the app lets you set up wake-up alarms, and it also features its own digital clock face. (Or, if you prefer, you can use any other app, and the sounds will continue to play in the background).
Price: $3 (iPad), $2 (iPhone)