I tried to promote this game in my cute Japanese Android game roundup last year, and I'm at it again: You should probably play Nekonoke if you like cute cats in your video games.
Unlike the other games on this list, Nekonoke is more a tapper game than an idle game, asking you to keep tabs on it often to rake in money. And how do you make money, you ask? By tapping hairballs off your cats, of course!
Nekonoke's charm lies not only in the adorable kitties, but also in the too-cute music and slow but real sense of progression. It takes a while to really progress because cats and furniture, not to mention their upgrades, get expensive fast. But that's part of the fun that keeps you coming back.