First off, to think that God needs my money in order to do his will is ludicrous. What I mean is that it is ridiculous for me to think for a second that I am doing God a favor by chipping in my $200 or whatever every month.
In regards to tithing, I had the same question you did and did some research on it. In the OT, a tithe was required (because they were under the Law) of the Israelites. In my studies, I have yet to find this requirement stated in the NT. The reason I would then view tithing as not for today, is that, that Law was part of the ritualistic laws in that were implemented by God in the OT. Now, that does not mean that we are not to give to the church. Paul talks about giving in 2 Cor 8:1-15. He uses the Macedonians as an example to the Corinthians in regards to giving, which I feel we should follow their example.
v2-3 says, "...that in their great ordeal of affliction their abundance of joy and their deep poverty overflowed in the wealth of their liberality. For I testify that according to their ability, and beyond their ability, they gave of their own accord..."
I think it imperative to also take into account 2 Cor 9:6-7 which says, " Now this I say, he who sows sparingly will also reap sparingly, and he who sows bountifully will also reap bountifully. Each one must do just as he has purposed in his heart, not grudgingly or under compulsion, for God loves a cheerful giver."
This is all to say that we should be giving to the Church, however I do not see a strict 10% limit imposed on us. This is my conclusion:
"From looking at verses in the Bible, the concept of tithing is limited to the OT (in terms of a requirement.) As with most things in the NT, God's focus is on the heart, so it is with the giving of money to the church. Rather than God giving us a certain percentage (which I've been told could have been closer to 30%) he tells us to give as we see fit. Perhaps this way the focus is not on obeying a command (which is prevalent in the OT) but rather it is on your heart (which is a focus in the NT)"
-matt