This image of The Spinning Dancer pops up frequently in advertisements on ScienceBlogs. I find it fascinating. If I concentrate hard I can make the dancer switch from spinning right to spinning left (and vice versa) but I can't tell you how to do it and I can't always succeed.
How about you? Can you make her switch? Is it easy or hard? Do you prefer one direction over another? I my case, I have trouble switching her from clockwise spinning to counter-clockwise spinning but not the other way around.