Clash of Clans. My wife and kid are stuck with it it seems.
It's often tedious, but the clan and invaders keep things (barely) interesting enough.
Here's an interview with their #1 player:
http://forum.supercell.net/showthre...urrently-Rank-1-Clash-of-Clans-Player!-Part-1
I don't play it, but chip in from time to time. When you're online, enemies won't come. When you're offline, your town may be subjected to 1-2 attacks (on the average) per night.
Son and I are working on a simple Arduino tool to tap the iPad screen regularly so that the game doesn't disconnect. Grrreat parenting.