1 John 3:17 (NKJV)
But whoever has this world's goods, and sees his brother in need, and shuts up his heart from him, how does the love of God abide in him?
This is plain; material blessings on the child of God constitute a responsibility to help those in need. This verse does not necessarily limit those whom you help to a brother in Christ. However, if you see someone in need who is not a believer, first give them the opportunity to receive Eternal Life. But seasoning that message with some material help in their hands will help them to "hear" your love.
I don't use this same "needs" based criteria for ministries however. There are lots of ministries who "need" my donations. My responsibility there is not to respond to the need but rather to use Henry Blackaby's Experiencing God principle to "find out where God is working and join Him there." It may be that the reason the ministry is in need is that God wants to shut it down for some reason. You'd be hindering God's plan if you supported such a "needy" ministry. This is just common sense. The scriptural basis would be the parable of the talents. God expects a return on his investment. By poorly investing you spoil the return.
The bottom line however is obvious. Your giving ought to be in line with the degree to which you are materially blessed. And the degree to which the gift is a sacrifice is the degree to which it is an act of love.