This article is from the Storms FAQ, by Chris Landsea email@example.com with numerous contributions by others.
The reason is that the earth's rotation sets up an apparent force (called
the Coriolis force) that pulls the winds to the right in the Northern
Hemisphere (and to the left in the Southern Hemisphere). So when a low
pressure starts to form north of the equator, the surface winds will flow
inward trying to fill in the low and will be deflected to the right and
a counter-clockwise rotation will be initiated. The opposite (a deflection
to the left and a clockwise rotation) will occur south of the equator.
NOTE: This force is too tiny to effect rotation in, for example, water
that is going down the drains of sinks and toilets. The rotation in those
will be determined by the geometry of the container and the original
motion of the water. Thus one can find both clockwise and counter-
clockwise flowing drains no matter what hemisphere you are located. If
you don't believe this, test it out for yourself.