And unto him that smiteth thee on the one cheek offer also the other; and him that taketh away thy cloak forbid not to take thy coat also. Give to every man that asketh of thee; and of him that taketh away thy goods ask them not again.
Give to him that asketh thee, and from him that would borrow of thee turn not thou away.
I read once about Jewish "anti-missionaries" who used this passage to get Christians to give away clothes, Bibles, and so on. I wish I'd been there, because in honor of this verse's context, you bet I'd give to anyone who "tooketh" away my stuff -- and then, I'd call the police.
Let's start with the Lukan passage. One thing to keep in mind here is that in the first century, if someone larger and stronger, or with a bigger club, took away your stuff, there wasn't a whole lot you could do about it -- and you couldn't dial 911 (or would it be, with the Romans, IX-I-I?) and have the cops come over and fill out a crime report, then go out and put the crook in the slammer. The Romans were too busy and/or apathetic to address such matters as petty crimes among the commoners (they were mainly concerned with protecting the rich and stopping rebellion and riots), and even if the sheriff was around, chances are that whoever it was who robbed you was some sort of bandit in the wilderness who knew how to make a getaway.
You might have some luck with the Sanhedrin, of course, but even these guys, if you were poor, were likely to reply to you with no more than a contemptuous sniff (as in the story of the unrighteous judge).
Now perhaps you could fight back, of course; or you could go find the crook (good luck!) and either haul him to the authorities yourself, or demand your stuff back ("ask" here carries the sense of demanding; more likely you're demanding your stuff back right after it is taken); and of course you'd start a fight in the process...and that's the point, and why Luke paired this saying with the one about the personal offense of cheek-smiting -- the point here is, don't escalate the violence. And that's the way a believer would have to do it, since there was no proper way for justice to be administered -- the only authorities around didn't care or weren't likely to be much help even if they did.
Today, of course, we have police and the courts to deliver God's justice; this passage speaks to us today against taking the law into our own hands and against vigilantism. I would say as well that it does not forbid self-defense if you are able to fight the crook off -- the point is, let justice rest in the hands of those with whom it is invested by God (Rom. 7).
This leads to the slightly different element of Matthew 5:42. Read woodenly this would suggest giving away things without discernment, but the two parts of the verse are actually in Hebrew parallelism and are two ways of saying the same thing. [Bivin and Blizzard, Understanding the Difficult Words of Jesus, 11] "Ask" and "borrow" in Hebrew are synonyms in a certain sense: A difference is made in Hebrew between borrowing something tangible (a book or a coat) and borrowing something interchangeable (money, flour, etc). Jesus uses the two different senses in this verse: "Give to him that asketh thee (for a thing like a book or a coat), and from him that would borrow (flour or money) of thee turn not thou away."
But now pair this with the teaching in 5:39 on revenge. The teachings belong together: One way to "get even" with a neighbor would be to refuse to extend them a loan. I.e., when Fred Flintstone is mad at Barney Rubble, one way he shows it is my refusing to let Barney borrow his bowling ball. In a corporate society such as the ancient world, such refusal to exchange or loan violated a common precept of survival and concern for the common good. It is only by removing this verse from its larger didactic and social context that one can read from it a justification to go up to a Christian and "ask" for their radio, Bibles, etc. just to get them to "follow" this command.
So, if you ever have these verses used on you, it doesn't mean you'll be going stark naked for the sake of someone trying to make a point -- and if anyone does try to apply the verses, in the way the Lukan context suggests and contrary to the Matthean context, remind them that larceny and assault equates with 10 to 20 in the state pen.