First, Jesus didn't say 'lie down and get walked on' or 'run away' or 'lie your way into pleasing the guy that hit you' or 'lick the guy's boot'. He said to turn the other cheek. Now, why?
Let's add a little history. In Jesus' time, the left hand was unclean, used for things that toilet paper is used for today, it wasn't used for much of anything else, if it could be helped. Therefore, in order for someone to have gotten hit on the right cheek by someone facing them, the striker would have had to have used the back of the hand.
A back of the hand blow was a blow that signified the punishment of a child, a woman, or a slave, all of which, in that era and time, were second class citizens. Lower than the lowest man of that time. To be hit that way implied an insult, a degradation.
To turn the other cheek, then, was an implied demand for acknowlegement of equalness. To get hit on the left cheek with the right hand required, first, that the striker acknowledge the striken as something that wasn't of a lower class, wasn't dirt beneath his heels but a real man. Second, it does imply that one shouldn't return bad for bad, violence for violence.
In many ways, it's a lesson of assertiveness versus agressiveness. It is not a lesson that advocates passivity in the face of abuse. Protect your own rights and priviledges without destroying anothers. It's a good balance, too many people can be badly agressive, destroying other people's peace, property or rights in the pursuit of their own. That's wrong. Assertiveness is the protection of your own without hurting anyone else.