When building a prototype of a device, it's common to use a solderless breadboard into which you can poke the legs of through-hole components for temporary electrical connectivity. Sometimes, though, even this is too fiddly, particularly when dealing with young children. Commercial systems like littleBits and Snap Circuits aim to make things easier for little hands, but if you're looking to build something using less-common components - or are building to a tight budget - you're out of luck for off-the-shelf solutions.
Matthew Dalton has a simple solution to the problem in the form of an Instructable for building quick-connect circuit blocks. Based on the same principle as littleBits, each component is built from only four parts: a wooden carrier block, a pair of strong magnets, a length of copper tape, and the component itself. Designed to form part of an electronic board game Matthew is designing, the blocks allow for circuits to be build in three dimensions using any components of your choosing - even, if you're handy with a soldering iron and have some spare wire, surface-mount devices.
The secret behind the circuit blocks' ability to be quickly connected and disconnected? Rare-earth magnets, embedded on all sides at the end of each block. These glued into place then covered in copper tape, which provides the electrical connectivity: simply bring the ends of two oppositely-polarised pieces together and they'll snap gently into place - or not-so-gently, depending on the magnets you've chosen - and complete the circuit.
The beauty of Matthew's design is its simplicity: unlike commercial variants, the wooden circuit blocks can be built using cheap material and using any component you might need for simple educational circuits. Add a block with a battery holder, and you've got a fully-custom educational kit at a fraction of the cost of commercial equivalents.
I was working on making a collaborative board game where people would build circuits. It went through many revisions, saw many rule changes, and made it pretty far in development. Sadly, difficulties with certain aspects of the rules, and other projects requiring my attention at the time kept me from moving forward any more on this. While this won't tell you anything about the game (as I'd like to get back to working on it someday), I will tell you how to make the pieces I used to snap together circuits.