Pixel Dungeon: Roguelike, infinitely replayable. https://play.google.com/store/apps/details?id=com.watabou.pixeldungeon
Auralux: A simple real time strategy game. https://play.google.com/store/apps/details?id=com.wardrumstudios.auralux
2048: Simple to learn, difficult to master puzzle. https://play.google.com/store/apps/details?id=com.androbros.puzzle2048eng
As would FFXIV.