Scavenger Hunt
A Bible-theme scavenger hunt is fun for smaller children. They may not yet grasp all the concepts you are teaching them, but you can use items from the lessons they are learning, hide those items and have the children hunt for them using Bible-based clues. For instance, you can ask a question such as "How many of eat animal did Noah bring on his ark?" When the kids collectively answer the question correctly, they get another clue to find an item.
Charades
Charades is a classic game that can be played in both large and small groups. You can have the kids guess people from the bible, events or places. It is best to stick with one category, since each is so broad.
Spin the Bottle Trivia
Have the kids sit in a circle and spin an empty soda bottle in the middle of the circle. Whomever the bottle points to must answer a Bible trivia question. If the child answers correctly, he stays in the game, but if he answers incorrectly, he is out. The last kid remaining is the winner.
Who Am I
Write the names of people from the Bible, one on each index card, and put tape in a loop on the back of each card. The kids will draw a card without looking at the name written on it and stick the card to the back of their shirt. Have them mingle among one another and ask questions about the character listed on the card. For instance, they may ask, "Am I a women?" or "Am I a disciple?" By asking questions, they can attempt to guess their identity after each question is answered. When they guess the identity of the person, they can sit and watch the remaining players.