Why do clocks run clockwise and not counterclockwise (or anticlockwise for those that use that term)? The short answer is for the same reason that north is always up on maps. The civilizations that developed maps and dial clocks were from the northern hemisphere, and for that bias, that's the way things developed.
So why did northern civilizations make clocks run the way they do? It has to do with a sundial. In the northern hemisphere (north of 23.5° north latitude), the shadow of the gnomon on a sundial will appear to move from west through the north to the east as the Sun crosses the sky. Looking down on the shadow, it seems that the shadow is moving clockwise, hence, why clocks run this way.
In the southern hemisphere (south of 23.5° south latitude), the shadow would appear to move counterclockwise. Therefore, if clocks were developed there, clocks would probably run counterclockwise.
Strange things happen, however, between 23.5°N and 23.5°S. At the equator, a sundial would run counterclockwise when it is spring and summer in the northern hemisphere, i.e. the Sun is north of the celestial equator. When the Sun is on the equator, the shadow only stays on an east-west line (never points north or south). In the southern spring and summer, the Sun is south of the celestial equator, and therefore, a sundial would run clockwise. This works for any latitude between the Tropic of Cancer (23.5°N) and the Tropic of Capricorn (23.5°S). When the Sun is north of your latitude, sundials run counterclockwise. When the Sun is south of your latitude, a sundial will run clockwise. And when the Sun is at your latitude, the shadow stays on an east-west line.