The Rattleback

The rattleback is a transparent "Celtic stone", or semi-ellipsoidal top, that, when given a gentle flick with a finger will spin easily in a counter-clockwise direction.  However, when given a similar flick in a clock-wise direction, the rattleback will execute a few CW turns, then stop turning and rock back and forth, then begin to turn in a CCW direction, seemingly defying the laws of physics.  This effect works most dramatically when the rattleback is sitting on a hard, smooth surface, such as a glass surface, to minimize friction and allow the rattleback to spin freely.

Check the references below for a variety of explanations of this phenomenon.