Hurricanes are blown around the planet by the prevailing global winds. When a hurricane forms in the Atlantic Ocean, it comes together in a band of winds called the trade winds, which blow east to west in the low latitudes. Once a hurricane approaches land, local weather conditions become a much larger factor in its movement. In particular, high pressure zones can stall or divert a hurricane from its path.
If a hurricane moves above 30 degrees latitude, it may encounter the subtropical high, a relatively stable high pressure air mass over the eastern Caribbean. If it passes around this high pressure center, it encounters the westerlies, a band of winds that blow southwest to northeast. This is why hurricanes that turn northward before they reach the United States often bend back around to the northeast, missing the country entirely.
Similarly, cyclones in other parts of the world are subject to similar wind patterns. Those that form in the eastern Pacific are blown westward by the trade winds toward Asia, or they make it through the Pacific subtropical high and swing northward. Cyclones that form in the southern Pacific move westward as well, but a similar band of westerlies exists to curve errant storms to the southeast. Storms that form in the Indian Ocean exist in a region without strong wind patterns, and therefore are extremely unpredictable in their movements.