Scavenger Hunt
Take your 2-year-old outside. Go to a park, in your yard or to another natural environment, and give him a short list of simple items to find. For example, a blade of grass or a yellow flower. Get your child to run around and find these items. This will keep her active, but also engage her mind in looking for the objects. Make sure you supervise your child well during the scavenger hunt.
Ball Games
A ball game is a simple and entertaining active game for your 2-year-old. Play either outside or inside, as long as you stay clear of any fragile objects. Straight-forward ball games are best for a younger child. For example, catch or kick a ball to each other. When the ball gets dropped, or rolls away, ask your child to go and collect it, as this will keep him even more active.
Dancing Games
Dancing is something that almost every 2-year-old can enjoy, and it is very active and healthy. Make a game of it by playing musical statues, where you pause the music and your child has to stop still like a statue. Alternatively, if she's too into the groove to want to stop, make suggestions of things for her to dance like, such as a kangaroo or a fierce lion.
Simon Says
Simon Says is a versatile game your child can enjoy for years to come. It's ideal to play indoors on a rainy day, when you can't be active outside. Alternatively, you could move the game outside if you wanted more space. If you act as "Simon" in the game, you can give your 2-year-old some active instructions to follow. For instance "Simon says, 'jog on the spot'" or "Simon says, 'jump up and down.'"