Like dodgeball with multiple balls, and there are no teams, so everybody is a target. And here’s the big twist: when someone gets you out by hitting you with a ball, you remember who got you out, then if later that person gets out, you go back in! This keeps the people who are “out” interested in the game. The game usually goes on forever, although it is possible to be the last one standing.
Start with 3-7 balls on the floor in the center of the hall/room/field, and all of the kids out of bounds around the sides (or touching a wall). Then yell, GO!
The usual rules apply: if the ball is caught in the air, the thrower is out instead. If the thrower hits someone in the head, the thrower is out. You can deflect a thrown ball with a ball that you are holding and you are not out (but neither is the thrower). You could limit the number of balls that one person can have at one time, although watching someone try to run around holding four balls is pretty amusing.
You may want to choose softer balls, especially if you’ve got some really big guys who can throw really hard. We use a variety of balls, like slightly-deflated four-square balls, plus a few nerf balls.