Badminton is a game of subtle skill. It's a perfect activity for the whole family, sure to get the competitive juices flowing. For more spontaneous outdoor entertainment that requires no setup time, go for footballs and basketballs. Toss the kids the ball and off they go. They'll be worn out by sundown.
When you can't entertain the kids with garden games any longer, it might be time to plan a bigger adventure. Round up the camping equipment and set off into the countryside. You'll need camping stoves and tents to keep the crew fed, dry and warm through the night.
A roof rack is a great way to easily load up the car with all your extra equipment. Some have fittings to transport the children's bikes, so you don't have to squeeze them into the boot. After a day of cycling through the woods, you'll all sleep soundly under the canvas.