This question would seem to be one of simple physics, and yet it continues to engender sharp disagreements. The main problem here is the division between theory and practice: whereas in principle the earth's rotation could affect the direction of draining water, in the real world that effect is probably swamped by other, less uniform influences.
Brad Hanson, a staff geologist with the Louisiana Geological Survey, presents the argument of why--in theory--water going down the drain would indeed spin in different directions depending on which hemisphere you're in:
"The direction of motion is caused by the Coriolis effect. This can be visualized if you imagine putting a pan of water on a turntable and then spinning the turntable in a counterclockwise direction, the direction in which the earth rotates as seen from above the north pole. The water on the bottom of the pan will be dragged counterclockwise direction slightly faster than the water at the surface, giving the water an apparent clockwise spin in the pan. But if you were to look at the water in the pan from below, corresponding to seeing it from the south pole, it would appear to be spinning in a counterclockwise direction. Likewise, the rotation of the earth gives rise to an effect that tends to accelerate draining water in a clockwise direction in the Northern hemisphere and counterclockwise in the Southern."
Fred W. Decker, professor emeritus of oceanic and atmospheric science at Oregon State University notes, however, that the Coriolis effect may actually have little to do with the behavior of real-world sinks and tubs:
"Really, I doubt that the direction of the draining water represents anything more than an accidental twist given by the starting flow. The local irregularities of motion are so dominant that the Coriolis effect is not likely to be revealed. An empirical test could help."
Robert Ehrlich, a physicist at George Mason University, expands on these ideas:
"Do bathtubs drain in different directions in the two hemispheres? If you had a specially prepared bathtub, the answer would be yes. For any normal bathtub you are likely to encounter in the home, however, the answer is no.
"The tendency of a circulation in a fluid to develop in a clockwise direction in the Northern Hemisphere and a counterclockwise direction in the Southern Hemisphere can be traced to the earth's rotation. Imagine a cannon fired southward from any latitude above the equator. Its initial eastward motion is the same as that at a point on the spinning earth. This initial eastward velocity is less than that at a point later in its trajectory, because points closer to the equator travel in a bigger circle as the earth rotates. Therefore, the cannon shell is deflected westward (to the right), from the perspective of a person standing on the earth. A gunner firing a cannon northward would find that the shell is also deflected toward the right. These sideways deflections are attributed to the Coriolis force, although there really is no force involved--it is just an effect of being in a rotating reference frame.
"The Coriolis force accounts for why cyclones are counterclockwise-rotating storms in the Northern Hemisphere, but rotate clockwise in the Southern Hemisphere. The circulation directions result from interactions between moving masses of air and air masses moving with the rotating earth. The effects of the rotation of the earth are, of course, much more pronounced when the circulation covers a larger area than would occur inside your bathtub.
"In your tub, such factors as any small asymmetry of the shape of the drain will determine which direction the circulation occurs. Even in a tub having a perfectly symmetric drain, the circulation direction will be primarily influenced by any residual currents in the bathtub left over from the time when it was filled. It can take more than a day for such residual currents to subside completely. If all extraneous influences (including air currents) can be reduced below a certain level, one apparently can observe that drains do consistently drain in different directions in the two hemispheres."