Churches often make a distinction between "tithe" and "offerings" saying the tithe is what you give to the local church and the offering is what you give above and beyond. This sounds somewhat legalistic, but it isn't.
Deuteronomy 14:22-29 is where the law spells out the tithe, and here is what it says (NIV):
Eat the tithe of your grain, new wine and oil, and the firstborn of your herds and flocks in the presence of the LORD your God at the place he will choose as a dwelling for his Name, so that you may learn to revere the LORD your God always.
But there is a caveat in the law:
But if that place is too distant ... exchange your tithe for silver, and ... buy whatever you like: cattle, sheep, wine or other fermented drink, or anything you wish. Then you and your household shall eat there in the presence of the LORD your God and rejoice.
So the tithe was given for a feast. This tithe was not given to a local church, it was not given to the temple, it was used for a feast to remember how God has blessed us through the year. But if we did this it too would be legalism.
But some people say that the tithe was not abolished from the law in the New Testament, but this is also not true. Acts 15:28-29 says:
It seemed good to the Holy Spirit and to us not to burden you with anything beyond the following requirements: You are to abstain from food sacrificed to idols, from blood, from the meat of strangled animals and from sexual immorality. You will do well to avoid these things.
So the tithe is not compulsory for the Christian. But what about principles from the Old Testament, don't they hold some weight in our lives? Yes. The most quoted text I can think of regarding giving is Malachi 3:8-10:
"Will a man rob God? Yet you rob me.
"But you ask, 'How do we rob you?'
"In tithes and offerings. You are under a curse—the whole nation of you—because you are robbing me. Bring the whole tithe into the storehouse, that there may be food in my house. Test me in this," says the LORD Almighty, "and see if I will not throw open the floodgates of heaven and pour out so much blessing that you will not have room enough for it.
This passage is one showing an angry God. In verse 5 God says, "So I will come near to you for judgment ... against those who defraud laborers of their wages, who oppress the widows and the fatherless, and deprive aliens of justice, but do not fear me." Going back to Deut. 14 we learn that the "storehouse" is where the tithe of the third year goes "so that the Levites (who have no allotment or inheritance of their own) and the aliens, the fatherless and the widows who live in your towns may come and eat and be satisfied." (v. 29) It seems this tithes and offerings in Malachi God said was being robbed from Him was what went to sustain the alien, orphan and widow. This has a New Testament precedent in James 1:27:
Religion that God our Father accepts as pure and faultless is this: to look after orphans and widows in their distress and to keep oneself from being polluted by the world.
But still, what do we make of the New Testament as it pertains to giving? It seems pretty clear in 2 Corinthians 9:7 that, "each man should give what he has decided in his heart to give, not reluctantly or under compulsion, for God loves a cheerful giver."
There is only one place in the New Testament that directly references a tithe, and it is speaking of how Jesus is a High Priest in the order of Melchizedek (Hebrews 7), not about our own tithe. But Christ and the Apostles are clear that the Christian should give, and generously, out of joy and for the comfort of those in need. In fact, in the Parable of the Sheep and the Goats (Matthew 25:31-46), Jesus said that judgment would be coming to those that did not give, "I was hungry and you gave me nothing to eat, I was thirsty and you gave me nothing to drink" - while there was glory for those that did give, "I was hungry and you gave me something to eat, I was thirsty and you gave me something to drink."
So the Christian should give, but not out of compulsion. They should give to whom they decide, and there isn't a specific place or amount we are called to give.