Goats are among the world most playful farm animals. They are also very useful for products such as milk and cheese, not to mention meat, but you can't play with a dead goat. There are several way you can engage in play with your adult and kid goats.
Placing objects in such a way that make a natural jungle gym is way to engage the explorer in every goat. Grab a log and place it against a tree, put a wooden see-saw in the pen, or just get a few objects to climb on like large rocks, dog houses and tree stumps. There have even been goats known to play on trampolines. Be mindful of any item that may be harmful to your animals and always observe objects completely before allowing free use. Goats love to climb, bounce and jump.
Goats are intelligent, inquisitive and impulsive, so keeping them busy is important of you don't want them to go bonkers on your expensive fences or flower beds. They love to chew so find a few things they like. A goat will absolutely lose it's mind over a ball, they love them. Basketballs, soccer balls, and volleyballs are all great options. Tying a rope to ball securely and tethering it to a post or pole can provide hours of fun.
If your a person of larger stature and don't have large goats then playing head butting games is very entertaining for you and your goat. This is a risky game for you since a larger goat could possibly do you harm, but if the risk is worth it, or you have very small goats, then go for it. Simply place your hands around your goats horns and push. It's just like a game of tug of war with a dog, except your pushing. This is not recommended for a young child to do, since it can be dangerous. Be creative but also be safe.