No need for flames. Even those of us who don't believe ought to be able to accept wise words and parables.

Along those lines, I'd like to offer a link to Walter Wink's Beyond Just War and Pacifism: Jesus' Nonviolent Way. There's something to glean here, even if you don't believe in Jesus.

Quoting from http://www.cres.org/star/_wink.htm (where there's a good bit more on this theme)

Turn the Other Cheek

"If anyone strikes you on the right cheek, turn the other also." Why the right cheek? A blow by the right fist in that right-handed world would land on the left cheek of the opponent. An open-handed slap would also strike the left cheek. To hit the right cheek with a fist would require using the left hand, but in that society the left hand was used only for unclean tasks. Even to gesture with the left hand at Qumran carried the penalty of ten days' penance. The only way one could naturally strike the right cheek with the right hand would be with the back of the hand. We are dealing here with insult, not a fistfight. The intention is clearly not to injure but to humiliate, to put someone in his or her place. One normally did not strike a peer thus, and if one did the fine was exorbitant. The Mishnaic tractate Baba Qamma specifies the various fines for striking an equal: for slugging with a fist, 4 zuz (a zuz was a day's wage); for slapping, 200 zuz; but "if [he struck him] with the back of his hand he must pay him 400 zuz." But damages for indignity were not paid to slaves who are struck (8:1-7).

A backhand slap was the usual way of admonishing inferiors. Masters backhanded slaves; husbands, wives; parents, children; men, women; Romans, Jews. We have here a set of unequal relations, in each of which retaliation would be suicidal. The only normal response would be cowering submission.

Part of the confusion surrounding these sayings arises from the failure to ask who Jesus' audience was. In all three of the examples in Matt. 5:39b-41, Jesus' listeners are not those who strike, initiate lawsuits, or impose forced labor, but their victims ("If anyone strikes you...wants to sue you...forces you to go one mile..."). There are among his hearers people who were subjected to these very indignities, forced to stifle outrage at their dehumanizing treatment by the hierarchical system of caste and class, race and gender, age and status, and as a result of imperial occupation.

Why then does he counsel these already humiliated people to turn the other cheek? Because this action robs the oppressor of the power to humiliate. The person who turns the other cheek is saying, in effect, "Try again. Your first blow failed to achieve its intended effect. I deny you the power to humiliate me. I am a human being just like you. Your status does not alter that fact. You cannot demean me."

Such a response would create enormous difficulties for the striker. Purely logistically, how would he hit the other cheek now turned to him? He cannot backhand it with his right hand (one only need try this to see the problem). If he hits with a fist, he makes the other his equal, acknowledging him as a peer. But the point of the back of the hand is to reinforce institutionalized inequality. Even if the superior orders the person flogged for such "cheeky" behavior (this is certainly no way to avoid conflict!), the point has been irrevocably made. He has been given notice that this underling is in fact a human being. In that world of honor and shaming, he has been rendered impotent to instill shame in a subordinate. He has been stripped of his power to dehumanize the other. As Gandhi taught, "The first principle of nonviolent action is that of noncooperation with everything humiliating."

EDIT: formatting