The Bible does not anywhere indicate that tithing is applicable or expected in our time at all. It was a system which was brought in following the exodus from Egypt and the forming of the children of Israel into a nation of their own.
Their nation was divided into 12 tribes, and 11 of these tribes grew crops, had animals, inherited land etc. The twelfth tribe, Levi, were the priests and administrators of the nation, and had no land, animals, crops etc, so the 11 tribes had to give the tribe of Levi 10% of their income. This mathematically works out that they were then all equal, because from this part which was given to the tribe of Levi, they still had to make their own offering of a tenth to God, the same as the other tribes had to. (see Numbers 18:25-39)
The tithing to give to the Levites was basically playing the same part as our taxes do today - our taxes pay for the everyday administration of our country. The Levites did everything from attending the tabernacle/temple, judging disputes, dignosing illnesses, being the judicial system etc.
Tithing was part of the old law, or what is sometimes referred to as 'the law of Moses'. It was given specifically to the nation of Israel, God's chosen people:
Ezekiel 20:10 "Therefore I led them out of Egypt and brought them into the desert.
11 I gave them my decrees and made known to them my laws, for the man who obeys them will live by them.
12 Also I gave them my Sabbaths as a sign between us, so they would know that I the LORD made them holy."
The law of Moses was a law of sacrificing to God for the atonement of sins. This was looking forward to the time when the one true sinless Lamb, Jesus Christ, would be offered to atone for the sins committed by Adam and Eve. When Jesus came, and as a sinless sacrifice for our sinful nature, he fulfilled the old law by his sacrifice and brought in a new one, referred to as 'the law of Christ'. The old law was then complete, it was obsolete.
Romans 10:44 "Christ is the end of the law so that there may be righteousness for everyone who believes."
Tithing was part of the old law which was done away with. We cannot continue with parts of the law which we choose, the old law was gone. The Jews continued with the old law because they refused to recognize the true position of Jesus Christ, that he was he was God's only son. So if we keep on with parts of the old law, we are doing the same. We as christians have never been under the old law, it was only following the rejection of Christ by the Jews that we, as 'Gentiles' were given the opportunity to be part of God's plan.
Money was definitely donated for the purpose of supporting very poor members in Jerusalem, but never to pay to a leader so that became his income.
Voluntarily helping someone, as the Macedonian brethren did for Paul, is quite different from tithing. We should be aware of others needs, and when we see the opportunity to help privately, then we should do so. The message of the New Testament is that our offerings in God's service should be voluntary and that no amount is set, and that the accumulation of wealth, even by a church, is not right. Rather we should give to the poor.
One of the very great dangers of churches demanding tithes is the accompanying perceived threat or fear that acceptance by God depends on the amount of money given. That acceptance is something money cannot buy. Often pastors of churches who tithe are very wealthy people - at the expense of their congregations, yet they often claim that they are wealthy because they have been blessed by God! Yet Paul could say, "I will very gladly spend for you everything I have and expend myself as well......I have not been a burden to you." (2 Corinthians 12:16).