One possibility would be to have a magnet attached to some kind of cup or sail, and within a coil. Any movement of the magnet induces electric current in the coil, which can then be harnessed.
Another possibility would be to use a gimbal, like a gyroscope. This could be used to house a rotor and blades (as from a conventional horizontal-axis wind turbine), keeping the rotor always pointing towards the wind. Alternatively, the gimbal could be set up with blades such that the wind turns the gimbal rings. At each joint of the gimbal would be a generator to harvest the rotory motion.