Alledgedly, we drive on the left because, back in days of old when knights were bold, it was better to keep your sword arm to the oncoming - and perhaps hostile - traffic. The story has it that because Napoleon was left-handed, he preferred the opposite side...
In fact, though, it seems that keeping right was codified in France at the time of the Revolution, and Napoleon at best spread it to the countries he conquered; it's said that nobility travelled on the left in pre-Revolution France, while the peasants travelled on the right for the same reason pedestrians are advised to today. Come the Revolution it wasn't healthy to be identified as a noble, so they switched to the right...
A more prosaic explanation might be practicality. It's also said that keeping on the left evolved because wagons and coaches are driven from the right hand seat, and keeping left made it easier to pass on narrow roads.
Supposedly, the switch to keeping right in some countries was made as a result of using teams of horses on heavy wagons, artillery etc. controlled by a lead horse which would be ridden; because horses tend to be mounted from the left the lead horse would be on the left, so it was easier to pass left to left.
I have never ridden a horse nor driven a wagon or stagecoach, nor was I in pre-Revolution France or the middle ages (though I feel that old sometimes) so you may take this with a pinch of salt.
Interestingly, when the Swiss army ordered heavy tank transporter tractors in the 1950s they were built right hand drive, as it was felt that seeing the edges of the road on the mountain passes was quite important...