Which side of the road is the proper side of the road to drive on, the left or the right?
Actually there is a right side of the road to drive on and it's not the right side, which is more properly the wrong side. The left side is the right side.
I'd previously thought that it was the Romans who gave us the answer but it seems that the Greeks & Egyptians show us what's right; for the same reasons.
Imagine that you are a Greek soldier. You have a sword and a shield. The commander of an army wants to make best use of his resources and so it makes perfect sense that he would want every soldier to carry a sword in the same hand. Since most people are already right handed, Greek soldiers like the Romans a couple of centuries later, were all right handed.
If everyone carries a sword in the same hand, then each soldier can huddle more closely together. The Romans who borrowed heavily from the Greek tradition of fighting, refined the Greek phalanx formation and turned it into their own Testudo or Turtle formation. By lining up shields as closely together as is possible, a unit can defend itself better against arrows. Thus, if every soldier carries a sword in the same hand, a Testudo can be formed quickly and efficiently; thus, reducing the time that cracks exist between shields and hopefully saving troops' lives.
Having every soldier carry their sword in the same hand also aids transportation. If chariots pass each other on the road and for some reason a fight breaks out, the driver would want to be on the side of the chariot which would allow him to defend his passengers. This means having your sword on the outside rather than in the middle had you been seated on the other side of the chariot; since soldiers are already right-handed, it is their right hand side which passes down the centre of the road; thus chariots and carriages would pass down the left hand side of the road.
This left hand side road rule would remain unchanged for centuries and so there wasn't really a need to codify it until traffic volumes rose. In England a general rule for London Bridge was made in 1756, signed into law with the The General Highways Act of 1773 and later confirmed with the Highway Act of 1835.
In fact the earliest evidence that I can find for any country switching sides, curiously isn't America even though given the fervent nationalism of the new nation. Empress Elizabeth of Russia issued an edict in 1752 which established a keep right rule. Post revolutionary France introduced a keep-right rule in 1792 and this was later consolidated by Napoleon.
If Russia and France were indeed the first nations on mainland Europe to standardize which side of the road they traveled, then for other nations to join them also seems understandable. Also given the cordial relationship that France had with America (them both being England's enemies) then for America to join France on the other side of the road as a symbolic gesture of solidarity, is again understandable.
In America, the Philadelphia and Lancaster Turnpike which opened in 1795 used a keep right rule and the States of New York and New Jersey followed suit in 1804 and 1813 respectively.
The spread of left and right hand side road rules seems to follow the expansion of empire as you'd expect, with mainly ex-British and Commonwealth countries remaining on the left hand side. The anomaly is Japan who maintained a practice that samurai passed each other on the left on horseback, with their swords on their left side.
So which is the safer side of the road? Statistics suggest that there is no difference in terms of safety when you look at accidents per 100,000km traveled, or such a small difference as to be negligible. The question then is of national fervour and patriotism and to that end of course I'm going to say that the left hand side is best because not to would be to admit that the French are right; since they drive on the right, then that's wrong and left is right.