Do we have to tithe? Why does God need us to tithe? What are the results of NOT tithing?
The strongest words with respect to the benefits of paying tithing, and the consequences for not doing so, can be found in Malachi 3: 8-12:
However, it appears that in the Christian period, just as with many other provisions of the Law, tithing was superseded by a higher law. Towards the end of both Acts 2 and Acts 4 it explains that the Christian community had all things in common, consecrating not a tithe (tenth) of their belongings but instead everything they owned to the general welfare of the church in order to do away with poverty. (It's worth noting that, while there are many obvious differences and incompatibilities between Christianity and communism, Karl Marx's famous "from each according to his ability, to each according to his need" was inspired by this part of Acts.)
The location of the chapter break between Acts 4 and Acts 5 is unfortunate, as Acts 5 begins with a direct continuation of the discussion of the treatment of the consecration of property that Acts 4 ended with. Here we see the story of a man and his wife who sold their property and gave part of the money to the Apostles, but kept back part of it to enrich themselves. Apparently the Lord takes this very seriously, (Galatians 6: 7--God is not mocked,) as He struck both of them dead when they tried to reaffirm their lie when questioned by Peter!
I'm not aware of any church today that practices this doctrine of total consecration, but the principle is still there. At the very least, a true believer should be willing to give up all that he posesses if it is needed to further the Lord's cause. (See Matthew 13: 44-46, Luke 18: 18-25, and especially Luke 18: 29-30 for the Savior's own words on this matter. See also Luke 12: 34/Matthew 6: 21--"Where your treasure is, there will your heart be also." The entire point of the Gospel is to improve our hearts and turn them towards heaven instead of the things of this world.)
I take 'why do we have to tithe' a step further:
By requiring the tithe, God is teaching us to put our trust in Him over money. So HAVE TO should be WANT TO.
I know this question has an accepted answer but it seems that one scripture has been missed:
In the words of Jesus "These you ought to have done, without leaving the others undone." In the NIV translation it says
One argument for not tithing is that it is a jewish law and we are not bound by it any more. While it is true we are not bound by the law tithing came before and was made into law.
(also read Genesis 14:20)