I was intrigued by this same issue, and so did some research on it. Some of my work is based on research by Ernest L. Martin (his work here), and some is from what I worked on my own. Following is a summary of what I found.
The Mosaic Law was very specific, the aspect of the tithe being no different. The tithe was instituted so that the tribe of Levi would be supported because they owned no property and could not raise crops or livestock. If you read the details of the tithe you'll see it specifies crops and animals. These tithes were to be brought to the Temple in Jerusalem and put into the storehouse. This was modified slightly, but basically that was it. In Malachi there is a description of them NOT doing this. There is no mention of contributing money even though there was money then; some people did work for money. The only time money is involved is if the person lives so far away from the Temple that it would be impractical to bring the animal or crop tithe. In that case, they were to sell their tithe, travel to the Temple, and then purchase the proper tithe. That was what the money changers, the ones Jesus drove out and threw down their tables, were there for. An important detail that is often missed or ignored was that this was for the nation of Israel only, not for the gentiles.
In the new testament Paul never mentions the tithe. The monetary sharing among the believers was on a local level, to those that had need. At one point Paul does help gather a large sharing for Jerusalem from among the believers in Corinth and the surrounding area, because there was a famine in Israel. This is done only once, and it is not referred to as a tithe.
There is actually less validity today for the tithe than there is for honoring the Passover. That's because the Passover meal isn't dependent on any conditions, so for a person still following the law honoring the Passover is okay. But the tithe is dependent on conditions. There is no longer a tribe of Levi conducting religious work at the Temple - there is no Temple. So to tithe as described in the Mosaic law is actually illegal today because there is no way to send it to the Temple.
I hope this helps.