If global weather generally moves west to...

The average hurricane moves from east to west due to the tropical trade winds that blow near the equator (where hurricanes start). When a hurricane is still in the Caribbean, the tropical jet blows east to west, and the hurricane moves west to gain power.

By the time a hurricane reaches North America, it generally curves into a northerly direction, as a result of the Coriolis force (which forces a counterclockwise rotation) and steering winds at higher levels. Normal storms, on the other hand, move west to east due to the strong jet stream.

Naturally, being nature, hurricanes do not always follow this pattern. In June, 1989, Pacific Hurricane Cosme traveled across North America and became Atlantic Tropical Storm Allison. In July, 1985, Hurricane Bob crossed Florida from west to east, tracked north along the Florida coast, made landfall on the southern coast of South Carolina as a tropical storm, and finally traveled north through western Virginia.