Reconfigurable gaming input device
The reconfigurable gaming input device would be shipped in kit form, with instructions on how to assemble the device from components. It would most likely be made of a microcontroller (ie PIC or AVR) with a USB interface. The microcontroller would support multiple modes of input. The directions would show different ways to configure the buttons/potentiometers to create a game pad, joystick, or other input device.
The physical hardware might consist of household objects. So a stick of wood could become part of a joystick. A book with buttons attached could be the makings of a gamepad.
The idea is to give the user as much flexibility in the creation of the gaming device as possible, while keeping the cost minimal. You would have to program in a lot of flexibility into the code (different modes, etc. for different devices), make it low-power, rugged, kid-proof, etc. and come up with a good gallery of sample devices and configurations you could build with this kit - I think the last 2 or so weeks of the project term should be spent just using the finished kit and coming up with crazy things to do with it (possibly recruiting a couple of local needham middle schoolers for the ride).
Evanwyk has done some ridiculous stuff with minimalist electronics (pins on a micro sensitive enough to print capacitive sensors straight on the pcb, etc) and might be another good person to hit for tech advice once you have an idea of what you want to build.