Why do you fall over if you close your eyes and stand on one leg?

I have tried several times, and I do not fall over. Still, to answer your question: I guess that your eyes register that you are standing straight, and as such you can keep your balance. When you close your eyes, the balance-organ in your ear is apparently not able to recognize a balance, and you fall. Also, I think that the muscles in your (one) leg aren't used to standing on their own. When you stand up, the muscles in your legs constantly make tiny adjustments to keep you standing. Normally, your legs would do that together, but now that one leg you're standing on has to keep balance all by itself. It's like the difference between riding a bicycle or a one-wheeler.