Cut the Rope arrived in 2010, early enough in the App Store's life to define what a touchscreen puzzle game should feel like. You swipe to cut ropes and physics delivers a piece of candy to a small green creature. That's the whole game and it sold over a billion downloads.
The design lesson here is about input. Cutting a rope with a finger is a gesture that feels correct in a way that no button press could, and ZeptoLab built every mechanic around things that are satisfying to do with a hand - swiping, tapping, blowing air with a bubble.
Om Nom is a very well-judged mascot. He does nothing except wait, blink and eat, and he generates enormous affection through animation alone. His disappointment when you fail a level is a genuine motivator.
The physics puzzles escalate properly too, layering spikes, magnets, air cushions and rockets over the same core interaction.
This collection covers Om Nom and his candy. Small, green, and permanently hungry.