Point&click adventures are my favorite genre and they play great on a tablet (on a smartphone not so much).
Although a few of them play even better on my Vita with the nice combination of input methods (touchscreen + sticks + buttons), Grim Fandango for example.
Mobile games I really like:
- Cut the Rope series
- Where's My Water/Mickey/Perry... series
- Monument Valley
- The Room 1 - 3
- Badland 1 + 2
- Rayman games (Jungle Run, Fiesta Run, Rayman adventures)
- République
- Ace Attorney series (1, 2, 3, 5 HD)
- Telltale Games seasons (Sam & Max, Tales of Monkey Island, TWD, TWaU, Game of Thrones...
- Daedalic games (Edna & Harvey, Deponia, The Whispered World...)
- Lost Horizon, Secret Files Tunguska + Sam Peters
- Broken Sword games (1, 2, 5)
- Blackwell games
- The Longest Journey Remastered
- The Journey Down 1 + 2
- The Silent Age
- realMyst