I have never seen a hard and fast rule of 10% explicitly stated in the New Testament as a commandment. This matter of tithing is similar to the discussion of the Sabbath (See my Q&A about the Sabbath). The Sabbath was a type of our rest of faith (Hebrews 4), and has been since replaced with the first day of the week for worship (Acts 20:7). The New Testament shouts aloud of our freedom in Christ. We aren't bound by ritualistic observances. The reason the Sabbath was supra-ritualistic is that God related it to His creation week in Genesis. This distinction made it more of a higher law than a mere ritualistic one. Such higher laws have fulfillment in the New Testament and some sort of replacements. I believe the idea of the tithe also transcends ritualism because God references it as an acknowledgment of Him being the owner of all things and king over all creation. In the Old Testament we see the importance of the tithe:
1) Abraham gave king Melchizedek a tithe of all he had, in honor of God the "possessor of Heaven and earth" (Gen 14:18-20). Hebrews 7 extensively discusses the tithe from Abraham to Melchizedek as being a tithe offered to one far greater than the Levitical priesthood -- namely Christ, the high priest of the order of Melchizedek.
2) In ancient times, the tithe was an acknowledgement of your submission to a king. The usage of consecrated tithes existed among the Greeks, Romans, Carthaginians, and Arabians. In 1 Samuel 8 we have the account of Israel demanding a king. God warned the people that a king woul demand ten percent from them (1 Sam 8:15-17). This shows that ten percent was normally due to the king -- whether earthly or heavenly.
3) Jacob (Israel), as an acknowledgement of Jehovah's protection and provision, vowed to give a tenth (Gen 28:20-22). This vow was not an obligation placed on Him by God, but rather a vow he made to God by his own volition. Has not God been faithful in providing our needs? Are we not Jacob's descendants spiritually (Gal 3:29, Rom 9:6)? Based on our identity in Jacob and God's faithfulness to Jacob and his descendants, it would follow that we should vow to God in a similar manner (at least in a similar willingness, if not amount)? Perhaps our vow should be even more than ten percent since we have a better covenant than ancient Israel, established on better promises (Heb 8:6).
4) Jesus acknowledged that the tithing of the pharisees was a noble thing, but they were ignoring the weightier matters such as mercy, faith, etc. (Mt 23:23) -- I do understand that this is not an extremely strong argument for or against the tithe, since this narrative occurs prior to His establishment of the New Covenant (and vanishing of the Old), being prior to Christ's death.
5) Proverbs 3:9-10 tells us "Honour the LORD with thy substance, and with the firstfruits of all thine increase. So shall thy barns be filled with plenty, and thy presses shall burst out with new wine". I believe that Proverbs are directly relevant for today, as many of them are quoted directly in the New Testament. Part of Proverbs 3 is even quoted in Hebrews 12. Therefore I have to believe that this proverb is useful and profitable -- a general principle for all time. It doesn't give a specific percent to give, but it does claim that we should give of our income back to God, and thus "Honour" Him. In addition, by doing so, God will fill our barns with plenty. It is a beautiful picture of Matthew 6:33 -- seek His kingdom first, even financially (prior to spending a dime for anything else) -- Give of our first fruits back to the very owner of it all. Jesus said, "For where your treasure is, there will your heart be also" (Mt 6:21). If our heart places Christ first, then we will naturally give the "first fruits" of our income back to God as an acknowledgment of Him being first in every area of life, including financial. If we spend our money on our own pleasures, and then see what is left for God, we demonstrate that His kingdom is not a priority in our lives.
With these emphases in mind, I believe the tithe (as the Sabbath) is fulfilled in Christ, yet replaced with giving on the first day of the week "as God hath prospered" us (1 Cor 16:2) -- a percentage based giving. Perhaps the percentage to give should be within the boundaries of Romans 14. If I feel the Spirit leading me to give more due to my prosperity, then I should give more. If I fail to heed the Spirit's prompting, and thus violate my conscience and spend the money selfishly, then I sin -- for anything apart from faith is sin.
Concerning the blessing of the tither/giver, I don't advocate or agree with "cursed if you don't tithe" preaching. We are redeemed from the curse of the Law (Gal 3:13) and free from the law of sin and death, as long as we are walking in the Spirit (Rom 8:1-2). However, I do believe that the general blessing of the giver (similar to the tither blessing in Mal 3:10 and Prov 3:10) is implicitly referenced in 2 Corinthians 9 ("he which soweth bountifully shall reap also bountifully"), as well as Philipians 4:19 ("God shall supply all your need according to his riches in glory [because they gave unto Paul's necessity per verse 16]"). The contexts of both of these passages pertain to the financial ministry to ministers, which is parallel to the giving of the tithe to support the priests in the Old Testament. The servants of the Old Testament (i.e. priests) were given monetary support for their services (Num 18:21, also see "meat in my house" in Mal 3:10). Similarly, the New Testament places an emphasis on supplying the needs of New Testament ministers. 1 Corinthians 9:9-14 makes it abundantly clear. If we sow sparingly in this area, we will reap sparingly financially (2 Cor 9:6), and vice versa. 2 Corinthians 9:7 does intimate that our giving should be done "cheerfully" (literally - hilariously) and not out of necessity. Yet, if it is cheerful for a believer to give one percent, while the pastor of the church is making poverty level income (as they do in many churches), such a "cheerfulness" is "sinfulness". Such a person should examine his heart. For this rule of giving "cheerfully" is common to New Testament obedience -- we love because He first loved us -- an obedience spawned out of sheer gratitude rather than compulsion. If the desire to give of your first fruits is not present, perhaps the gratitude for God's unspeakable gift is not present. I should give of my first fruits because God my king has provided all my needs, most importantly my need for salvation.
In conclusion, all New Covenant duties are rooted and grounded in the commandment of love -- to love God with all our heart, mind, soul, and strength, and to love our neighbor as ourselves -- Both of which should have inherent financial obligations to further the gospel, care for the needs of humanity, and for the servants of God. There is no specific mention in the New Testament as to who the first fruits should be paid to. Perhaps some feel led to spread their first fruits across multiple ministries and Christian charities. As long as our pastors, missionaries, and the poor are supported, then we are being led properly. Those with abundance should give to those who lack (See Acts 2:45, 4:35) -- a situation which we are VERY far from unfortunately. God forgive us!!