I believe tithing is applicable to believers today.
One of the big arguments against tithing is that it is part of the Law - however, Genesis 14 predates the Law by over 430 years.
I have personally claimed all the tithing promises and have seen God do His part by fulfilling the tithing promises. Would He do that if it was not for us today? We don't see Him consuming our sacrifices with fire from Heaven every time we lay them on the altar (hypothetical - I have not actually sacrificed any sheep in my backyard lately).
Malachi 3:8-11 Will a man rob God? Yet ye have robbed me. But ye say, Wherein have we robbed thee? In tithes and offerings. Ye are cursed with a curse: for ye have robbed me, even this whole nation. Bring ye all the tithes into the storehouse, that there may be meat in mine house, and prove me now herewith, saith the LORD of hosts, if I will not open you the windows of heaven, and pour you out a blessing, that there shall not be room enough to receive it. And I will rebuke the devourer for your sakes, and he shall not destroy the fruits of your ground; neither shall your vine cast her fruit before the time in the field, saith the LORD of hosts.
Notice it says "bring ye all the tithes into the storehouse" (not just some or part of the tithes). Also:
1 Corinthians 16:1-2 Now concerning the collection for the saints, as I have given order to the churches of Galatia, even so do ye. Upon the first day of the week let every one of you lay by him in store, as God hath prospered him, that there be no gatherings when I come.
Seems to be applying the OT storehouse to the NT church. Paul also refers to eating from the altar, using OT laws and principles to support taking care of the NT leaders of the church.
1 Corinthians 9:13-14 Do ye not know that they which minister about holy things live of the things of the temple? and they which wait at the altar are partakers with the altar? Even so hath the Lord ordained that they which preach the gospel should live of the gospel.
Proverbs 3:9-10 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.
Matthew 6:33 But seek ye first the kingdom of God, and his righteousness; and all these things shall be added unto you.
I have always applied this to seeking God on the FIRST day of the week, FIRST part of the day, giving Him my FIRSTFRUITS, as well as of course giving Him FIRST priority (not always successful, but that is what I believe I should be doing).
Yes, there were both freewill offerings and tithing under the Law, and we can see both referred to in the NT for the NT believer. For example, 2 Corinthians 8-9; Philippians 4.
One other thing worth considering for those who are not sure if the tithing applies today:
Here is a challenge for you. Read all the way through the book of Proverbs, and make a list of things that don't apply to you today (ie. don't apply to the NT believer). There is nothing that does not directly apply to us. Yes, there are references to sacrifices - but it is in reference to the sacrifices of the wicked, nothing about the righteous needing to offer animal sacrifices, nothing else ceremonial in that book - and nothing else that has been done away with or fulfilled in Christ - except for tithing (for the sake of this argument). However, if every other Proverb in the whole book applies to every believer today, perhaps tithing does too!