Square Enix just released Libra Eorzea, the free companion app for Final Fantasy XIV: A Realm Reborn, for Android devices. It was previously released only for iOS.
The application includes an in-depth database of quests, items and more, and lets you display your character and its equipment on your smartphone. According to Square Enix it will be expanded with further features in the future.
You can find it on Google Play, and see a few screenshots below.