My son and I enjoy playing this app called Clumsy Ninja. You can find it in the Google Play Store and I'm pretty sure they have it for Apple too.
You can take funny photos of your ninja in motion. There is even a cute feature that will let you take a photo of you and your ninja together.
It is set up like most games where you level up by completing tasks. Of course, there are extra things you can purchase with real money but I don't let my son do that.
Overall, I would recommend this app. My son is 6 now and has been playing it for a while. My phone's photo gallery seems to keep filling up with the ninja.
What are some of your favorite apps?