God games are particularly well-suited to mobile platforms, where the top-down interface lends itself well to touch controls, and the size of the screen - not to put too fine a point on it - helps with the deity fantasy. One of the more popular and unconventional latter entries in the genre is indie darling Godus from 22cans, published on the Play Store by DeNa. You can grab the free download now.
In Godus, you play as a god trying to nurture a stone-aged village to greater heights of civilization. This isn't done with direct control as in a strategy game: your primary power is shaping various layers of earth and water to make livable spaces for your followers. As they expand and increase their capabilities, your own power grows: you can soon bless crops and forests, enabling the population to grow and advance. And you can start fires (complete with brimstone!), because it wouldn't be a god game without a little smiting. The 3D visuals are intentionally sparse, almost like polygonal pastel paintings, which fits with the primitive theme.
Godus got its start on Kickstarter, and in fact it's still under active development as an Early Access Steam game on Windows and OSX. The reason people have been so eager to play it over the last year is that it comes from designer Peter Molyneux, famous for such titles as Dungeon Keeper, Black & White, and the spiritual progenitor of this game, Populous. The Android release gets all the features currently implemented on iOS (but not PC), including some basic multiplayer interaction through Facebook, which can link your "world" to others. There is currently a Facebook competition going on to celebrate the Android release - check it out here.
Godus is free to play, with the usual in-app purchases for game currency to spruce up your powers and followers. It's running rather sluggishly on my LG G Pad, but fine on my Nexus 6 - you might need considerable horsepower to get a good framerate.