Catch
A simple game of catch can be played with a baseball, basketball, tennis ball or any spherical object and can be played by two or more children. The game will test the children's hand-eye coordination. To add to the fun, implement a spelling game whereby if the students drop the ball they get penalized with the letter of a word, such as H from horse or D from donkey. The first student to get all the letters of the given word loses. Teachers can also choose to give the students a chance to have a letter rescinded by having the student answer a question.
Musical Chairs
Musical chairs is a fun game which simply requires school chairs and either a CD player, cassette player or even someone's voice to provide music. Several chairs are placed in a circle pointing outward and, as each round passes, one chair is taken away. The rounds pass as the music is stopped and the children run toward a chair. There should always be one less chair than there are children playing. The game requires children to have quick reaction times. One by one, the child which ends up with out a chair is removed from the game until only one is left -- the winner.
Hopscotch
Hopscotch is perhaps the archetypal school playground game because any child can play it and because all that's needed is a piece of chalk with which to draw the hopscotch court on the ground. Hopscotch is played by hopping methodically through the hopscotch court to collect a marker which has been thrown into it. Some variations of the game include singing a song or clapping as you go along to add to the difficulty and testing children's coordination by getting them to do several things at once.
Tag or Duck, Duck, Goose
Perhaps the most simple of school games and the only one which requires absolutely no equipment whatsoever, Tag is popular with school children the world over. The aim of the game is for the child who is 'It' to try to tag any of the other children involved in the game by touching them with their hand. The classroom variation Duck, Duck, Goose involves students being sat in a circle while one student walks around them tapping students on the head and saying, 'Duck' for each child until they decide to call a student, 'Goose.' At that point the 'Goose' must get up and chase the other student back to their seating spot. Whoever arrives at the vacant spot first is the winner. The other player then becomes It and the play starts anew.