In a graduate course I am running with some folks we host a creativity challenge every class. One challenge the teachers liked a lot was a paper bridge challenge. The basic idea is you get 1-2 pieces of paper and maybe some other stuff (e.g. 2 paperclips, or a strip of tape) and you have to design a bridge that can hold as many pennies as possible.
The teachers loved the simplicity and the variety of design options that they discovered. Its a great activity to kick off a unit on engineering design, physics, or building technologies. If you are looking for a resource to get started, check out PBS Learning Media's website. They have a video of students talking about their experience building a paper bridge and there are teacher links.