The habit of driving on the right was developed by teamsters (operators of horse-drawn carriages) in the United States and France.2
Back in the 1700s, horse-drawn wagons were needed to carry large amounts of equipment. Teamsters would sit in the left-back corner of their carriages, allowing them to use their right arm to whip the horses.
With the right being their established side of the road, American car manufacturers followed suit and made their cars with the drive side on the left.
As it stands, only four countries in Europe drive on the left, while countries that rely on car imports from America also tend to favour the right.