Tithing is the Old Testament duty of giving one-tenth of one's earnings and/or resources to God. The word tithe comes from the Old English word, "teotha", which means a tenth.  The Old Testament word translated tithe is the Hebrew ma'aser. The New Testament word translated tithe is the Greek apodekatoo.
"Every tithe of the land, whether of the seed of the land or of the fruit of the trees, is the LORD's; it is holy to the LORD." (Lev 27:30 ESV) "You shall tithe all the yield of your seed that comes from the field year by year." (Deut. 14:22 ESV)
Is tithing applicable to the N.T. Church?
Some say "Not as such"
Tithing in the sense of a requirement to give a "tenth" to God is part of the Old Testament Law. It is not taught as such in the New Testament. The only times "tithing" is mentioned in the New Testament, it is referring to usage under the O.T. economy. When the New Testament speaks about "giving," it goes against "tithing" as a doctrine or a legalistic requirement.
The apostle Paul also says in 1 Cor. 16:2, "On the first day of every week, each of you is to put something aside and store it up, as he may prosper, so that there will be no collecting when I come." (ESV) This is not tithing, only giving as one has purposed in his heart and as one has prospered, you choose the amount.
Again in 2 Cor. 9:7, Paul says, "Each one must give as he has made up his mind, not reluctantly or under compulsion, for God loves a cheerful giver." (ESV) There is no amount mentioned, it is what you have settled in your own heart.
Some say "Yes"
The following is taken from The Geneva Institute for Reformed Studies "Under the Old Testament priestly system the tithes and offerings were to be brought to the priests who acted as the elders of Israel to provide for and oversee the worship, to counsel and discipline the members, and to care for the needy in the covenant community. The admonition of Malachai 3:10 to bring the whole tithe into the storehouse, reminds us that the tithe is to be distributed and used under the authority of God's church, not to the individual."
"In the New Testament this same principle continues with no change except that the temple services and priestly work were completed in Christ. The day of worship was set by the Apostles to the first day of the week based on the Roman calendar that was in use at the time. Therefore we see the worshippers instructed to bring God's tithes and their offerings to the Sabbath worship of the church (1 Corinthians 16:1-2 and 2 Corinthians 8-9)."