A great question. The 10% figure is derived from the practice of the tithe in the Old Testament. This, however, only formed a part of an Israelites giving, which may have been up to 27% or greater. When we come to the New Testament, the tithe only gets mentioned in negative contexts. I would sum up the New Testament’s teaching on giving as being: Generous, Willing, Sacrificial, and Responsible. Paul writes:
For if the readiness is there, it is acceptable according to what a person has, not according to what he does not have.
2 Corinthians 8:12
So our giving is meant to be proportional to our wealth, which is a great freedom. Paul goes on:
The point is this: whoever sows sparingly will also reap sparingly, and whoever sows bountifully will also reap bountifully. Each one must give as he has decided in his heart, not reluctantly or under compulsion, for God loves a cheerful giver.
2 Corinthians 9:6-7
On the one hand, we are called to rich generosity, but to do so willingly and cheerfully, not as a command and burden. In these chapters Paul patterns Christian generosity on the generosity of God, in Jesus, who became poor for our sake (2 Cor 8:9).
However, there is a call for responsibility as well. Again Paul writes:
But if anyone does not provide for his relatives, and especially for members of his household, he has denied the faith and is worse than an unbeliever.
1 Timothy 5:8
Christians are also to consider their responsibilities and how they can meet and provide for them. Rich generosity for others should not lead to neglect and deprivation for those under our care.
In the end, Christians figure this out as a matter of wisdom: assessing their finances, their responsibilities, and then seeking to be as generous as they can, imitating the character of God who is a generous giver. This attitude, of course, goes way beyond just money. It includes all the resources that God has given us including our possessions, skills, wisdom and (most importantly in our time-poor society) our time for sake of others.