Depending on which way you see this dancer spin, this site claims to know which side of the brain you prefer. If she spins clockwise you are right-brained, counter-clockwise and you are left-brained.
The moving dancer and the full site are here.
This is the same as the classic box trick to the right (in which you are able to 'flip' the direction of the box), but more complicated because it is moving.
This test assumes some things in how we process visual information in relation to hemisphere dominance. The information from our right eye is processed through are left hemisphere, exactly the opposite with our left eye; this is why, depending on which way the dancer is spinning, the test assumes what hemisphere is dominant. The test also assumes that a right-brained person will turn the 2D image above into a 3D image (and have a harder time 'flattining' it in their mind), which makes it appear to turn clockwise.
The problem with this is that, even if your right-hemisphere is dominant in interpreting vision information does not mean it is dominant in other areas. Most people will see the figure move clockwise because most people right hemispheres do most of the visual processing.
Plus, the right-brain/left-brain dichotomy is no longer taken too seriously in the scientific world; current evidence shows that all reasoning processes are more integrated then we originally thought (so logic incorporates creative thought, and creative thought incorporates logical reasoning.) Mathematicians, for instance, must incorporate an incredible amount of creativity with logic and ‘hard’ math based skills of their field (Einstein, for example, was known for his incredible creativity.)
Still, it is fun to see which way the dancer moves, and to try to change her direction. I find it helps to look at the foot she is spinning on.