Square Enix have announced The Square Enix Market which will be avaliable on Android devices, as long as you’re in Japan and are a customer of KDDI, where the service will launch December 1st, or a DoCoMo or Softbank customer.
The games that have been announced so far for the Market include Final Fantasy (the iOS remake), Chaos Ring, Crystal Defenders and Dragon Quest Monsters Most Wanted! Chrono Trigger will also release in the market at some point in the future.
Though not announced outside of Japan, The Square Enix Market and any similar ventures should have an eye kept on them. If they prove successful there’s no reason why similar services couldn’t eventually make it in the West.