Time on clock, each minute hand that the second hand covers is 5 seconds.
5, 10, 15, 20, 25, 30, ..., 60
The point at which a runner passes the finish line in a 3000 metre race.
200m, 600m, 1000m, ..., 2600m, 3000m
Sound waves or waves in the sea are sinusoids, so they can repeat their pattern for the range of the sinusoid.
Half life of carbon or any element. You can then show how all the carbon 14 is depleted over thousands of years.
A graph where logs is used is easy to read and can be almost linear, whereas if there is a geometric increase you can't even plot it on paper. Kids love this one, and understand it very quickly.
Puzzle: If a frog is 1 metre from a door and jumps halfway, and then jumps halfway again continuing to half its jump each time, will it ever reach the door? This displays limits and geometric decreasing functions and the idea that decreasing jumps results in infinitesimally small results over time.
Showing kids how much they pay on a mortgage at 5% interest rate for 10 years, 20 years and 30 years is very insightful and clearly displays geometric increase.