I enjoy Final Fantasy 5 on my phone. It has rebooted graphics with added voice acting. Pretty cool. The FF tactical rpgs are very good. Many of the popular retro JRPGs are available on smart phones.

My roommate has been playing Fallout Shelter on her phone and she loves it. It's sounds like a typical tower defense game -- you have to manage your offense and defense and production of resources and all that stuff. FWIW, she's a very casual gamer.