IIRC the ancient Greeks typically fought in phalanxes, tightly organized formations of men with shields and spears. Each man's right side was protected by the shield of the man to his right. Unless the phalanx was broken, or you were the unlucky rightmost man.
Here is part of a wikipedia entry. I realize you can't blindly trust wikipedia, but this is the same as what I learned in the military history classes I took in college.
http://en.wikipedia.org/wiki/Phalanx_formation
Individual hoplites carried their shields on their left arm, protecting not themselves but the soldier to the left. This meant that the men at the extreme right of the phalanx were only half-protected. In battle, opposing phalanxes would exploit this weakness by attempting to overlap the enemy's right flank. It also meant that, in battle, a phalanx would tend to drift to the right (as hoplites sought to remain behind the shield of their neighbour). The most experienced hoplites were often placed on the right side of the phalanx, to counteract these problems. There was a leader in each row of a phalanx, and a rear rank officer, the ouragos (meaning tail-leader), who kept order in the rear. The phalanx is thus an example of a military formation in which the individualistic elements of battle were suppressed for the good of the whole. The hoplites had to trust their neighbours to protect them, and be willing to protect their neighbour; a phalanx was thus only as strong as its weakest elements. The effectiveness of the phalanx therefore depended upon how well the hoplites could maintain this formation while in combat, and how well they could stand their ground, especially when engaged against another phalanx. For this reason, the formation was deliberately organized to group friends and family closely together, thus providing a psychological incentive to support one's fellows, and a disincentive through shame to panic or attempt to flee. The more disciplined and courageous the army the more likely it was to win - often engagements between the various city-states of Greece would be resolved by one side fleeing before the battle. The Greek word dynamis, the "will to fight", expresses the drive that kept hoplites in formation.
There is a historian named Victor Davis Hansen who has written on the ancient Greek military techniques. One of his books is "The Western Way Of War", quite readable. He has become rather political and is something of a right-wing favorite, but this book was written back when he wasn't a talking head.