Freeze!
This game is best played with older kids in the nine- to twelve-year-old range. Gather everyone in a circle and pick two volunteers to start. Ask for suggestions about who they are and what they're doing to get the initial scene going. The two actors can get started after that, whether they're dinosaurs at Disney World or their grandparents at a concert. At any time, someone in the outer circle can yell "Freeze!" At this point, the two actors must freeze in whatever position they have taken. The person who shouted takes the place of one of the actors and begins a new scene from this position with entirely different characters, and it is the job of the other actor to pick up on the new story. It's best to talk to kids before the game begins about not calling "Freeze" too soon, or calling it without having a clear idea about what they want to do. The game can, unfortunately, end quickly if someone jumps into the fray and just begins to giggle.
Pass the Ball
This game is good for kids of all ages, and can be a great way of introducing improvisation to younger children. Have everyone sit or stand in a circle; standing tends to be better, but if you're worried about short attention spans, sitting can work as well. Join the group and pretend to be holding a ball. The ball, of course, is completely imaginary. Toss it up in the air, catch it and give the kids a real sense of the ball's weight and dimensions. Explain that it is a magic ball that can become heavy or light, and big or small, depending on who catches it. Pick the person next to you and tell them that when you pass them the ball, they have to take it as it is given (i.e., how you were acting with it), but that they can then have it transform into whatever kind of ball they want. This game is a good way to help kids learn about the basics of mime as well. They will begin to express themselves by staggering under the weight of a heavy ball, or bouncing a basketball against the floor, or throwing a football. As they get better, you can change the game from passing the ball around the circle to having them toss it to one another across the room.
One Sentence/Word Story
This improv game is especially good for younger kids, including those who are just learning about story structure. To begin, have everyone sit in a circle. Then, give the first sentence of a story. It can be anything from "It was a dark and stormy night" to "There were three people living in a yellow submarine." Go counterclockwise and have each child add a sentence to the story. It is sometimes helpful to speak with the group in advance to remind them that the story doesn't have to be too silly to be fun. Let the story go for about two rounds in the circle, depending on how many kids there are. When you feel it's reaching a logical end, you should be the person who wraps it up. As the kids get better at the game, you can start mixing it up. Let them think they can have a whole sentence, but in the middle of one shout "next!" and leave it to the next person to finish the thought. Eventually, you can have it to the point where each person is only adding one word to the story.