iOS: We're fans of using Dropbox to store your music files, but the official Dropbox app for iOS doesn't handle audio very well. Tunebox is a player app that makes your Dropbox a viable place for cloud music storage.
Tunebox has been around for a while, but a recent redesign really makes it shine. It's a simple music player, where you can search through your artists, albums and songs to choose the music you want. You can also download and save MP3s for offline play. You don't get the range of options you would with most alternative music players, but it does the job for simple music playback well, even when you're on mobile data. If you're storing your music in Dropbox anyway, Tunebox is worth a look.
Tunebox ($5.49) [iTunes App Store]