Nature Sounds Relax and Sleep (Android)
Start your personal audio therapy with this assortment of high quality, relaxing nature sounds, including thunder, ocean, birds, rain, waterfall, and more.

Relax Melodies: Sleep Sounds (iPhone | Android)
Designed with a good night’s sleep in mind, this app is for those who have difficulty getting to sleep or feeling rested in the morning. Beyond sleeping, the app is great for any situation that requires calming sounds or music, such as yoga.

Sleep Cycle (iPhone | Android)
An intelligent alarm clock that analyzes your sleep and wakes you in the lightest sleep phase – the natural way to wake up feeling rested and relaxed.

Deep Relax (iPhone)
A companion for sleep improvement, stress relief, yoga practice and meditation.

Relax & Rest Guided Meditations (iPhone | Android)
Designed with a good night’s sleep in mind

Not an app, but highly recommended by students:

Sleep With Me: The Podcast That Puts You to Sleep
The narrator delivers meandering, stream-of-consciousness monologues in a monotone that recalls the most boring teacher you ever had. Each hour-long episode sets out to bore its listeners to sleep, distracting them from their own thoughts with bizarrely earnest monologues on topics ranging from zombie songs to Dian​a Rigg to Ser Pounce, the royal cat from Game of Thrones.