Hide and Seek
This classic game will never go out of style, and you can play it in almost any area (except maybe a field). Define a safe playing area, have the child go and hide while counting to 60 and then go find him. Children love to try to out-think their babysitters, so this should provide enough entertainment without the little ones losing their interest. Just make sure the child knows that there are some places that are unsafe to hide in; make these boundaries before you start the game
Cat's Cradle
For this game, all you need is a piece of string and some know-how. Tie a piece of string so that it forms a loop, and create all different kinds of shapes while using your hands to keep the string tight. When playing with two people, the idea is to transfer shapes back and forth. Most kids enjoy this game and will want to learn how to do it themselves.
Hopscotch
Although commonly associated with young girls, this game is suitable for boys too and will provide wholesome fun while giving the children much needed exercise. All that is required is a piece of chalk and an open piece of sidewalk or driveway. Draw a series a squares for the children to jump to and the hopscotch board is complete. This is a great way to burn away some of that access energy stored up in the kids. Plus, most children already know how to play, so you don't have to spend time teaching them how to play.
Hand-Clapping Games
A babysitter and kid can play hand-clapping games. Simply using different clapping styles and a varying rhyme scheme will keep the kids interested. Use the standard rhymes, like Pattycake or Miss Mary Mack, or create your own rhyme and clap sequence. You can find other hand-clapping games online. (see Resources)