They don't. This is urban folklore, based on the fact that the Coriolis force causes large weather systems to rotate in opposite directions in the two hemispheres, if viewed from the same viewpoint--say, that of an astronaut in orbit. (The folklore was perhaps bolstered by an "X-files" episode in which Mulder noticed water in a sink rotating the "wrong" way.) Confusingly, from the point of view of the person or thing subject to Coriolis acceleration, the deflection is always to the right.
However, sinks and toilets are too small to be affected by the Coriolis force, which is a consequence of the curved surface of the Earth. That curvature is completely insensible on scales of a few inches or feet.
You can find more than you ever want to know on the topic in Wikipedia, includindg this limerick:
"On a merry-go-round in the night,
Coriolis was shaken with fright.
Despite how he walked,
'Twas like he was stalked
By some fiend always pushing him right."
– David Morin, Eric Zaslow, E'beth Haley, John Golden, and Nathan Salwen