I'm not personally a fan of video or computer games, so when my roommate (the one who has two feet) reccommended this app called Neko Atsume, I was reluctant. But yesterday, I downloaded it.
It is VERY cute.
It's not really a game. You don't do much, and neither do the cats. There is a yard where you place food and toys, and bags, etc. if see if they come. They won't if you are watching, you have to close it and come back periodically to see if you've been visited by a feline.
When they are there, you can take pics of them if you want for their album. Sometimes they leave you gifts, in return for the stuff you left out for them, and you can use that to "buy" more stuff. You can also use real money to buy things, but I'm not doing that. So far I've been visited by six felines.
I have an Android. I don't know if there is an iPhone version.
Anyway, it's adorable and gentle and very low key. Who among us doesn't get all gooey when we see a lovely kitteh???