As a small note to coffy's excellent writeup is that a slap by the left hand in Roman times was dishonor on those who did the slapping. For centuries, left-handedness was considered evil, and inferior.

There are several other references to right and left-handedness in the Bible, such as sitting on the right hand of God (no mention as to sitting on the left hand of God), being separated off into right and left (sheep and goats, as an example), and it is still debated which is which in correct interpretations, due to spacial perceptions).