You can't really play a console-level quality Destiny game on your iPhone, but with Shadowgun Legends it's about as close as you can get. This first-person shooter might be the best in the app stores, with a base camp (it's more of a city) where you can hit up shops to buy weapons and armor, a place to gamble for more in-game currency, a black market for new items, and so much more. There are tons of in-app purchases here, to be sure, but you can easily avoid them
