BBC has an article up today explaining how it is that Ouija board planchettes seem to move on their own. As I in fact mentioned back in 2009 in my novel Arcana, the explanation is simple - the board picks up small, imperceptible motions in your fingers and transfers them to the planchette. This is an observation that surprises absolutely no practicing magicians. It's obvious if you spend any amount of time working with a board that it's your fingers doing the movement. After all, there are some crazy stories and 1980's movies about planchettes moving on their own but I've never met anyone who's actually observed it. The article compares the use of a Ouija board with the motion of a pendulum, another common divination tool, and dowsing, which operates according to the same principle.
The phenomenon is called the ideomotor effect and you can witness it yourself if you hang a small weight like a button or a ring from a string (ideally more than a foot long). Hold the end of the string with your arm out in front of you, so the weight hangs down freely. Try to hold your arm completely still. The weight will start to swing clockwise or anticlockwise in small circles. Do not start this motion yourself. Instead, just ask yourself a question – any question – and say that the weight will swing clockwise to answer "Yes" and anticlockwise for "No". Hold this thought in mind, and soon, even though you are trying not to make any motion, the weight will start to swing in answer to your question.
Magic? Only the ordinary everyday magic of consciousness. There's no supernatural force at work, just tiny movements you are making without realising. The string allows these movements to be exaggerated, the inertia of the weight allows them to be conserved and built on until they form a regular swinging motion. The effect is known as Chevreul's Pendulum, after the 19th Century French scientist who investigated it. What is happening with Chevreul's Pendulum is that you are witnessing a movement (of the weight) without "owning" that movement as being caused by you. The same basic phenomenon underlies dowsing – where small movements of the hands cause the dowsing wand to swing wildly – or the Ouija board, where multiple people hold a cup and it seems to move of its own accord to answer questions by spelling out letters.