There are a lot of great things to do with your babysitting charges. Unfortunately, many of them cost money, which babysitters don't have.
These activities take little or no money, and use things you can generally find around the house.
Treasure Hunt (ages 4 and up)
Children love this game. You can simplify it for younger children by hiding an object somewhere in the house or even in a specific room and having the child find it. Let each child take turns hiding the object.
On slips of paper, write simple clues such as "go where books are kept." Then, let the children find the next clue of the same sort there (in a bookshelf), and so on until they reach the "treasure" which can be anything, like cookies, or a board game to play, or even a story you will read to them.
If you have children younger than 7, don't leave them in a room by themselves while you are hiding the clues. You can bring the children into each room with you and have them close their eyes, but don't leave them alone. This could also apply to children over 7, depending on the child. It is your call as the babysitter to do what is best for each individual child.
Paper Bag Guess (ages 3 and up)
Find a paper grocery bag, or a paper lunch sack. Find objects in the house that have a distinctive shape and feel. Put the object in the bag and let the children take turns feeling the object and guessing what is in the bag. Then let the children take turns putting objects into the bag and letting the others guess.
Silly Faces (all ages)
Stand the children up in front of a mirror. Have them make silly faces at themselves. Then have a contest to see who can make the scariest, happiest, saddest, maddest, etc. Be sure to let each child be a winner so that there are no tears.