Sprints
One of the first events the Greeks participated in were short sprints, called "stades." One stade was equal to the length of the stadium.
Foot Races
The Greeks thought that if you lost a race, it meant the gods didn't like you. There were different types of races. They ran both sprints and longer distance races, ranging from twice the length of the stadium to twenty-four times the length of the stadium. Another race was between two and four lengths of the stadium and was run by men in full armor. A way modern children might be able to race in a similar way would be to race each other wearing backpacks loaded down with textbooks.
Wrestling
As in modern wrestling, Greeks tried to pin each other to the ground. Unlike in modern wrestling, they were allowed to break each other's fingers in order to win.
The Long Jump
Still played today, the men would take a running start, arrive at a line drawn on the ground and see how far they could jump.
Javelin Throw
Part of five other events, which were called a Pentathlon, the javelin throw was where they would take turns throwing a javelin, which was made of wood and as tall as a man, as far as they could.
Discus Throw
Greek men took a disc, spun around in a circle and threw it as far as they could. Modern children could play this with a frisbee if they wanted to.
Field Hockey
While not part of the Olympic games, ancient Greek boys played field hockey.
Juggling
Greek girls were not allowed to participate in most sports, especially since Greek men and boys played them in the nude, but they were allowed to do some physical activities. Juggling was one of these.