I've seen some impressive demonstrations of machine learning and am definitely not claiming this as one. But I'm pretty proud of a kid I've been tutoring for a quite sometime now.
We created a simple simulation where a "muncher" would randomly move either left, right or jump to eat the randomly placed falling food. Through many iterations, the muncher would figure out the most efficient way to eat the most amount of food.
In the beginning, the muncher would aimlessly move around as shown below (muncher is the green dot, food is the falling blue dot):
But after sometime, the muncher started to figure out a more efficient way to get more and more food: