For the most part, traveling on the left side comes from British influence. It supposedly dates back to feudal days, when you may have had to defend yourself and wanted to have your right (weapon) hand nearest to an opponent.
Driving on the right came about during the horsedrawn era, when the driver of a large cart was usually mounted on the left, leaving his right hand free to whip the team. It was to his advantage to travel on the right side of the road, so he could better observe passing riders and vehicles as they went around him.
Once something is established, it's hard to get people to change. There are 166 nations where people drive on the right; 74 where they drive on the left.