Have you ever noticed that we can't hurt someone or do an injustice to someone without vilifying that person first? We can't do a dirty deed unless we've rationalized it. Part of the witness of Christ Himself was His "passive resistance" at His trial. By allowing us to do what we did to Him, He showed us our sins and shamed us. Had He resisted, we would have said, "Well, this man deserves it! Listen to how he spoke to the High Priest! Look at how angry he got! Listen to how he curses us from the cross! Look at how he spits back when we spit on him!"
But in accepting His persecution and in suffering willingly and for the most part silently - indeed in praying for us as we tortured and killed Him - He prevented us from convincing ourselves that we were in the right - or at least He inserted a lingering doubt. And as we jeered Him, maybe one or two of us felt a touch of shame.
Thus "resist not evil" and "turn the other cheek" is really an act of mercy toward the aggressor - it not only keeps you from losing yourself to wrath and giving in to the lust for vengeance, it keeps your enemy from the handy trick of convincing himself that he's justified in hating you and hurting you. Turning the other cheek is more for his sake than for yours.