The World Ends With you came out on the Nintendo DS in 2008, and it quickly became a surprising hit, reviving developer Square Enix in the minds of RPG fans everywhere. With the fresh setting of contemporary Tokyo, an art style inspired by graffiti, and a unique battle system that took advantage of the DS hardware, it's easy to see why. The enhanced iOS version came out almost two years ago, but as typical with Square releases, it's just now coming to Android.
If I had to describe the game in a single sentence, I'd say it's a turn-based RPG version of Jet Set Radio where teenagers play The Hunger Games in Hell. Yeah, that's about right. The story is the kind of incredibly confusing and overly complicated thing that anime fans seem to love, but what's really appealing is the game's visual and music style. In the battle sequences in between the story, you control the main character Neku directly while the computer controls an ally, and the two can team up to perform intense screen-filling super attacks.
Like almost all Square Enix games, The World Ends With You is phenomenally expensive in Android terms, weighing in at $17.99 in the US Play Store. Not only that, but it also includes in-app purchases. If you look at the iOS page, you'll see that the most popular IAP seems to be extra healing, crafting, and currency items (cheats, essentially) and music tracks. If the game is faithful to its Nintendo DS roots, none of them will be necessary to complete the story... but it's still in pretty poor taste to include IAP in a game this expensive. You can also earn in-game items by trading profiles with other players, and their profiles will appear as NPCs after you swap.