A spinning dancer, from news.com, via Freakonomics and Marginal Revolution (I'm giving those sources because you might want to look at the comments there.)
There is a woman spinning; the question is, is she spinning clockwise or counterclockwise? Supposedly this has something to do with which side of the brain you use, although I'm not sure I buy it.
But my first thought was "clockwise from whose perspective? From the perspective of someone looking from above, or from below?" (To clarify what I mean by "clockwise", I mean that the dancer is turning to her own right.) I think this does say something about my brain, namely that I demand precise definitions for terms, at least for the sorts of terms that can have them.
Some of the commenters at various places say that you have to look at the shadow, because the shadow doesn't agree with the dancer; as far as I can tell this isn't true, and this is not some sort of optical illusion.
The actual resolution is that you can imagine reflecting the dancer through the plane of your monitor (I almost said "the plane of the board", because usually when I'm thinking about three-dimensional pictures it's when I'm teaching calculus), which will change the direction of rotation but not the picture. So on an intellectual level I understand why both perceptions must be possible. But I can't see her going counterclockwise. Not at all.