I mostly play Point&Click adventures (LucasArts classics, Broken Sword series, Blackwell series, Gemini Rue, Broken Age, Syberia 1 + 2, The Journey Down, Bertram Fiddle, Infamous Machine, Runaway, Yesterday, Milkmaid of the Milkyway, Deponia, Secret Files, ...) and similar puzzle games (Monument Valley 1 + 2, The Room series, Ace Attorney series, Telltale Games episodes, Layton's Mystery Journey, Framed 1 + 2, Her Story, République, Ghost Trick...) on my iPad and Android tablet.
These kind of games work best on a touchscreen.