Some good critical thinking games are "If You Build It" and "Save the Egg." Additional critical thinking games that also add elements of fun are "The Worst-Case Scenario" and "A Shrinking Vessel."
"If You Build It" involves both critical thinking and teamwork. Groups of people work with a variety of materials, such as spaghetti, blocks or marshmallows, for example. Each group sets out to build the tallest structure possible using the materials. Changing the materials involved or changing the building task gives this task a number of variations for repeat use.
With "Save the Egg," each individual or group drops a raw egg from a specified height. The critical thinking element of the game is to design a structure in which to sit the egg. Ideally, the structure prevents the egg from breaking when it falls.
In "The Worst-Case Scenario," groups of people imagine that they are stranded at sea or lost on a desert island. In this game, the entire group is lost together. The group may choose 10 items to have with them, but they all must agree on the items. Each group then works on a list of must-have items that ensure the group stays safe and returns to civilization safely.
Similarly, in "A Shrinking Vessel," a group works together to solve a problem. In this case, the group stands within a defined space, such as within lines of rope or tape. Periodically, the group leader makes the space smaller. The group must figure out how to stay within the space as it shrinks below a comfortable size.