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About a quarter of the world drives on the left, and the countries that do are mostly old British colonies. This strange quirk perplexes the rest of the world; but there is a perfectly good reason.
In the past, almost everybody travelled on the left side of the road because that was the most sensible option for feudal, violent societies. Since most people are right-handed, swordsmen preferred to keep to the left in order to have their right arm nearer to an opponent and their scabbard further from him. Moreover, it reduced the chance of the scabbard (worn on the left) hitting other people.
Furthermore, a right-handed person finds it easier to mount a horse from the left side of the horse, and it would be very difficult to do otherwise if wearing a sword (which would be worn on the left). It is safer to mount and dismount towards the side of the road, rather than in the middle of traffic, so if one mounts on the left, then the horse should be ridden on the left side of the road.
In the late 1700s, however, teamsters in France and the United States began hauling farm products in big wagons pulled by several pairs of horses. These wagons had no driver's seat; instead the driver sat on the left rear horse, so he could keep his right arm free to lash the team. Since he was sitting on the left, he naturally wanted everybody to pass on the left so he could look down and make sure he kept clear of the oncoming wagon's wheels. Therefore he kept to the right side of the road.
In addition, the French Revolution of 1789 gave a huge impetus to right-hand travel in Europe. The fact is, before the Revolution, the aristocracy travelled on the left of the road, forcing the peasantry over to the right, but after the storming of the Bastille and the subsequent events, aristocrats preferred to keep a low profile and joined the peasants on the right. An official keep-right rule was introduced in Paris in 1794, more or less parallel to Denmark, where driving on the right had been made compulsory in 1793.
Later, Napoleon's conquests spread the new rightism to the Low Countries (Belgium, the Netherlands and Luxembourg), Switzerland, Germany, Poland, Russia and many parts of Spain and Italy. The states that had resisted Napoleon kept left - Britain, the Austro-Hungarian Empire and Portugal. This European division, between the left- and right-hand nations would remain fixed for more than 100 years, until after the First World War.
Although left-driving Sweden ceded Finland to right-driving Russia after the Russo-Swedish War (1808-1809), Swedish law - including traffic regulations - remained valid in Finland for another 50 years. It wasn't until 1858 that an Imperial Russian decree made Finland swap sides.
The trend among nations over the years has been toward driving on the right, but Britain has done its best to stave off global homogenisation. With the expansion of travel and road building in the 1800s, traffic regulations were made in every country. Left-hand driving was made mandatory in Britain in 1835. Countries which were part of the British Empire followed suit. This is why to this very day, India, Australasia and the former British colonies in Africa go left. An exception to the rule, however, is Egypt, which had been conquered by Napoleon before becoming a British dependency.
Although Japan was never part of the British Empire, its traffic also goes to the left. Although the origin of this habit goes back to the Edo period (1603-1867) when Samurai ruled the country, it wasn't until 1872 that this unwritten rule became more or less official. That was the year when Japan's first railway was introduced, built with technical aid from the British. Gradually, a massive network of railways and tram tracks was built, and of course all trains and trams drove on the left-hand side. Still, it took another half century till in 1924 left-side driving was clearly written in a law.
When the Dutch arrived in Indonesia in 1596, they brought along their habit of driving on the left. It wasn't until Napoleon conquered the Netherlands that the Dutch started driving on the right. Most of their colonies, however, remained on the left as did Indonesia and Suriname.
In the early years of English colonisation of North America, English driving customs were followed and the colonies drove on the left. After gaining independence from England, however, they were anxious to cast off all remaining links with their British colonial past and gradually changed to right-hand driving. (Incidentally, the influence of other European countries' nationals should not be underestimated.) The first law requiring drivers to keep right was passed in Pennsylvania in 1792, and similar laws were passed in New York in 1804 and New Jersey in 1813
I hope this detailed history now puts the matter to bed!