Godville 12+

It absolutely does not command your time or try and hook you in any way. There’s only one “in-app purchase” available and it’s something you get for free and don’t need, so it’s completely elective whether or not you choose to spend any money.
You can choose to play as little or as much as you want. If you want to play more, there’s a social aspect with guilds (some of which are very active) and a forum.
The coolest part is how player-made it is. It’s completely text-based, and all players are allowed to submit new ideas for any possible thing in game to an “ideabox.” Players then vote and later the developers go through and choose the ones they like. The amount of variety is insane—you could go days without seeing a repeat, and the majority is completely fresh every time.
Even more than that, there’s a GodWiki, which is basically Godville’s own little Wikipedia. Except it isn’t little, because it houses entries on everything under the sun, and again, almost all of the wiki is player written and reviewed. It’s kind of incredible how nicely the community works together to create new content.

I’ve been “playing” this game for 6 years and 7 months. I’ve forgotten about it for over a year and went back just to check on how many years it’s been running. I don’t actually use my godpower so I have tons of charges. There’s really nothing to do with the game but I have a good memory from the day I downloaded it so I haven’t deleted it yet. I also want to know how many years it’ll take me to get 100% of the bricks needed for the temple. I’m at 37.2% after almost 7 years so I may die before it happens.

It may not seem like it at first, but it's really fun to have minimal control over the game as it has a life of its own. The game is super funny and creative and the fact that the hero/heroine adventures even while you're away makes them seem like a real person. The best part about it is that you don't need to make time to play this game, and it's very entertaining when you're bored.