Balloon Art
For a messy and involved paint game, try using balloons and darts to create art. Any canvas size works for this, though a large area works better. Fill up balloons with whatever desired paint colors, using at least three or more colors. Tie the balloons, as you would with a water balloon, and pin them, without breaking the balloon, on a canvas. Space them at different intervals. Grab a handful of sharp darts and simply play darts with the canvas. The balloons pop and splatter the paint, creating unique and fun art. If you want to get really creative and have an old space, such as the side of a garage or shed, attach the balloons to the wall and "repaint" the wall using this method. This is a great project for older kids with supervision.
Jackson Pollock Art
An especially fun game with paint for kids is emulating Jackson Pollock's splatter-paint style. Not only is this a way for kids to learn about art history, but they will love throwing paint around the back yard. Be sure that you set up the canvas or white sheet far away from houses or cars. Grab as many paint colors as desired, and smother brushes in paint and and start splattering. This game can be as messy and creative as you want to make it, and the result is wild, colorful painting.
Twister Paint
For a kid's party idea, try a twist on the classic game of Twister. Create a Twister board by using a white sheet and painting small of red, green, yellow, and blue in vertical rows to designate the areas of the Twister board. Using whatever colors you choose, instruct each child to dip their hands and feet in paint. Play Twister as usual, and the kids will love playing a common game with a silly twist. At the end, admire the "board" they created.