LEFT
In olden feudal and violent times all the societies preferred left hand convention. It offered various advantages if one was right handed. One could -
-keep right weapon wielding hand closer to the opponent and scabbard away from him.
-avoid inconvenience of bumping into someone else's scabbard
-mount/dismount on horse easily. Since right handed men mount horse from the left (since scabbard is on left) keeping on left allowed one to dismount on edge of the road.
RIGHT
With new advents agricultural production started to rise transportation of crop became problematic. Immediate solution in US and Denmark was carts being pulled by multiple horses (higher horsepower, quite literally). The wagons did not have a seat and again, majority of right handed men decided to follow right hand convention. Going from right hand side of the road one could -
-ride the rearmost horse on the left, leaving right hand free to whip horses.
-easily monitor oncoming vehicles and their wheels which are coming from the opposite side
French Revolution, Napoleon, British and the mess that ensued:
In pre-revolution France the aristocracy traveled on the left, forcing peasant to use the right side. However, after revolution, to save themselves from the guillotine, aristocracy preferred walking on the right to keep low profile. Therefore right hand convention became unwritten rule in France.
Arrival of Napoleon messed the whole thing up. He started enforcing Right hand convention in all the conquered countries (Germany, Poland, Switzerland etc). Naturally, his opponents vehemently maintained the left hand convention, British being at the forefront. Europe was literally divided due to these conventions till first world war.
Road regulations were established everywhere in 1800s. British enforced left hand convention in all her colonies. That's the reason India and previous African colones still follow left hand convention (Egypt being exception due to Napoleon's conquest).
US had already amended laws to enforce right hand convention, to escape the British roots of origin. Right hand convention was gradually becoming more prevalent and further bolstered by mass production of American automobiles. British conservatives have resisted the homogenization of this convention obstinately.
Today only four European countries, including Britain, follow left hand convention. In 1960 even British tried to switch to right hand convention. However, the conservatives and involved cost proved to be too daunting to bring about the change.