Well, I've played a TON of Empires and Puzzles, to the point where my main (i.e the one on the phone in my pocket) has completed all the current content, but I'm still playing because it's reasonably fun to play and I like building my characters and stronghold up.

I keep going back to Fallout Shelter. It's not GREAT, but it's engaging, and it's one I can shut off and return to (a big plus, for me).

And... that's about it. Too many games are twitch based, for me, or don't deal well with "Dammit, I have to go change a poopy diaper."