Right-hand drive was born out of common sense.
In ancient times, when you walked past someone, you would want him
to be on your right. This is so that if he's unfriendly, you can
easily pull out your sword (on your left) and fight him.
When horses for transportation were introduced, most riders would
put his left foot on the stirrup and swing right leg over to the
other side. This was also because of the sword which was on the
left side of the body.
When the small carriages were introduced, they would travel on the
left hand side. This is to prevent the driver from accidentally
hitting pedestrians on his right while he's whipping the
horses.
It was the French who introduced left-hand drive. If I'm not wrong,
it was because of Napoleon choosing to start battles from the left
(or something to that effect).
The Americans chose left-hand drive as well. They used far bigger
carriages than the English which require the driver the sit on the
horse on the left hand side for greater control.
Someone correct me if I'm wrong.