The Coriolis Force
Clocks run a little slow in the northern hemisphere and a little fast in the southern hemisphere due to the rotation of the Earth and the effect of the Coriolis force.
Behind the Legend
For reasons too impossibly complex for a non-specialist to fathom, the middle of the Earth (sometimes called the "equator") moves faster than its top and bottom (the "poles"). This means that things near the equator (e.g. Egypt) will move faster than things farther away from the equator (e.g. penguins). This in turn means that if something is lying perpendicular to the equator, its bottom will move more quickly than its top, making it rotate. This is nicely explained (in layman's terms) in Chubby Checker's song, "The Twist."
Because Coriolis force, like gravity, is caused by a planet, it is mighty strong. Even so, it can not make clocks and watches (more specifically, ones with dials) run faster or slower unless they are held parallel to the ground so that there is a significant difference between the speed of their near-equator and far-equator edges.
Even so, this force does influence the world around us quite significantly, even if it doesn't bother watches all that much. For example, Coriolis force: