Do weather systems turn clockwise or anticlockwise?

Knowing which way the major air masses are turning is useful for looking at the synoptic maps because the positions of the highs and lows can give a guide to the general direction of the winds in your area and knowing which way the wind is coming from gives you an idea of the expected weather.

This Primefact explains the Coriolis force and the resultant wind movements around high and low pressure systems in the northern and southern hemispheres.