Why do hurricanes swirl?

Answer 1

See the related link to Coriolis Effect

Hurricanes rotate due to the Coriolis Effect, a product of earth's spin. in the northern hemisphere wind moving toward the Hurricane from the north will be deflected to the west, while wind coming in from the south will be deflected to the east.

It is different for tornadoes as they are too small to be significantly influenced by this effect. Instead what happens is the wind speed and direction change with altitude, a condition called wind shear, this sets some of the air rolling on a horizontal axis. This rolling can then be tilted into a vertical position by a thunderstorm's updraft. The rotation can then tighten and intensify to form a tornado.
The rotation in hurricanes and tornadoes comes fro different sources.

In a hurricane the low pressure draw air inwards across a very broad region. Since earth is spherical, it can be said to be "fatter" (relative to the axis) at latitudes closer to the equator. This means that they have to travel further in the same amount of time as earth rotates, or in other words must move faster. However, air traveling from one latitude to another will resist this change in speed. As a consequence, air drawn into a northern hemisphere from the north will be deflected to the west of the storm, while air drawn in from the south will be deflected to the east, resulting in a counterclockwise rotation. This is called the Coriolis effect.

However, on systems such as tornadoes and individual thunderstorms, which are much smaller than hurricanes, this effect is negligible. The rotation of a tornado comes from the thunderstorm that produces it. If a thunderstorm moves into a condition called wind shear, where the wind speed and direction varies greatly with height, it can cause the rising air within the storm to start rotating. If this rotating storm is strong enough the rotation can tighten into the more intense vortex of a tornado.

Answer 2

It's the Coriolis Effect!

http://en.wikipedia.org/wiki/Coriolis_effect

Note: Does not govern swirl of toilet water.