Jon Bloom at Desiring God has some good thoughts here and here regarding this very issue. He looks at the verse in Matthew 5:42 that says "Give to the one who begs from you, and do not refuse the one who would borrow from you." In the second of the two posts, he addresses the cynicism that surfaces within us when faced with the decision to give or not. And he clarifies what purpose Jesus actually has for our giving:
...the reason for our cynicism may be that we are misunderstanding Jesus' purpose for the command. We tend to assume that the motive for radical generosity ought to be to meet a real need and help facilitate transformation in someone's life. If that isn't likely to happen, we shouldn't give. It wastes money and reinforces evil behavior. The problem is Jesus doesn’t command us to give for those reasons.
What is his reason? "So that you may be sons of your Father who is in heaven" (Matthew 5:45) The point? The Father shows radical generosity toward both good and evil people (v. 45). The text makes no promise that all the evil people are reformed as a result of his generosity. From my observation, most are not.
And like Father, like Son. Jesus showed great kindness toward the crowds who followed him and toward those who crucified him. Yet only a few believed in him.
And like Father (and Son), like adopted "sons" (male and female). We are being called to bear the family resemblance. The Father’s children behave like the Father and the Son. One of those ways is the stunning—some would call foolish—way we show generous kindness toward undeserving evil people—the very kindness we’ve received.
If these evil people don’t repent, we are not wasting our generosity on them. Through us, God is showing them grace that he will hold them accountable for someday. We show the world that we love God and not money (Matthew 6:24). And God is showing us that he...is able to make all grace abound to [us], so that having all sufficiency in all things at all times, [we] may abound in every good work. As it is written, "He has distributed freely, he has given to the poor; his righteousness endures forever.” (2 Corinthians 9:8-9)Now, there are times when real love dictates that we withhold giving, and the more intimately we are involved in a person’s life the better we can discern this. Biblical love must govern all our actions. God give us wisdom!
It's also helpful to remember that Jesus is instructing disciples, not government agencies or NGO's. He’s not giving a formula for eliminating poverty. Neither is he necessarily instructing a church's institutional approach to community development, though he’s informing it. On those levels it is necessary to carefully identify and strategically address the causes of poverty.
But he is calling us to radical, gospel generosity. The kind that looks weird in the world. The kind that sifts our motives and tests our love. The kind that is impossible for the natural man. But let’s take heart, that’s the way it’s supposed to be, for “with man it is impossible, but not with God. For all things are possible with God” (Mark 10:27).