It is mostly due to the Coriolis effect (aka Coriolis Force). (Another reference here) Because of the Coriolis Effect, parcels of air (think of boxes of air) in the northern hemisphere are deflected to the right. This means that air around the subtropical ridge over the Atlantic ocean circulates clockwise.
Think of a tropical cyclone as a parcel, or box of air. It tries to complete the clockwise rotation around the subtropical high.
Now, inevitably someone will say 'Aha! I know of a storm that actually moved south.' Yes, different things can cause tropical cyclones to move in strange directions, such as the Fujiwhara Effect, other meteorological features. But by and large, the Coriolis force is the dominant cause of the curvature of the path of tropical cyclones.
It is also worth pointing out that the hurricane also has parcels of air inside of it. The Coriolis Force acts on that too, promoting rotation.