Peter Molyneux basically invented the "god game" with the advent of Populous, and returned to the scene with the recent Godus. But if you're looking for something similar to that adventure and need a breath of fresh air, there are plenty of similar simulation games where you can play god here and there. Just don't let it go to your head.
1. Pocket God
Pocket God is an oldie but a goodie, consistently updated with interesting additions and requiring a very low threshold for IAPs. There's hours of content from the very beginning as you take control of the God of a small island with a little tribe to take care of how you see fit. Each episode is comprised of a set of different objectives, and there's plenty to do when you factor in additional episodes that are available on a regular basis.
Download Pocket God for Android.
2. Tribes
Much like Populous, Tribes finds you taking charge of a landscape to invite settlers so they can build their own structures and live off the land as you choose for them to. It doesn't channel the same sort of good looks as Godus or any of the other titles on our list, but it's a deep and strategic title that anyone who grew up on Populous will want to try out, especially if you prefer more hardcore offerings that do less hand-holding.
Download Tribes for iOS.
3. Artificial Life HD
In this strange game, you lord over bacteria, each with its own hard-coded set of instructions. It's your job to make sure these miniscule bits of life survive beyond a few minutes. You create your very own virtual bacterium in one specific game mode, and in another you can set your own parameters for how your in-game universe will operate, then take the reins. It's a lot different than Pocket God or even Godus, but its bizarre premise is where it shines. You'll be saying the same thing once you see it in action, and then recommending it to everyone you know!
Download Artifical Life HD for iPhone.