Stick Ball Games
Classic Stick Ball is a simpler version of baseball that requires less equipment and can be played on any terrain. All that's required is a durable rubber ball about the size of your fist or slightly smaller and any variety of a stick roughly the length of your forearm or bigger. One person could hit a ball up against a wall repeatedly, but typically these style games involve two or more people. One should pitch and the other hit then switch off over a period of time.
Kickball and Soccer-Style Games
The most basic form of a ball game may be the kicking-oriented kind, since no equipment at all (besides a large rubber ball itself) is required and many children will find kicking a ball a natural inclination. For larger groups try a softball-style game with teams and specific positions for pitching, kicking and fielding. Smaller groups can try setting up makeshift goals and defending or scoring in the style of soccer.
Dodgeball Variations
This was the game that everybody loved (or hated) in high school and middle school gym class. The simplest form would involve a couple of kids throwing the ball at each other back and forth and trying to avoid contact if they are the one without the ball. Bigger groups should have several balls set in the center between teams or individuals which will then be grabbed once the game is started. Once children are hit they will be eliminated until another round.
Basic Bouncing Games
Any size or style of ball should suffice for this game, as long as it bounces. Large rubber balls can be bounced like a basketball or utilized, as in Four Square, for bouncing in individual zones. Smaller varieties can be used for playing Jacks or free bouncing in most kinds of terrain. Whatever the kind of ball, children can bounce it, then count how many times they can do so without stopping. The winner bounces the ball more times.