Should Christians tithe? Here's what I know.
After writing this answer, I did some research and eventually wrote a newsletter on tithing. That link has more complete information.
It seems clear from Scripture that tithing was not taught to the Church. Reading through the New Testament letters and Acts we can see that tithing is not mentioned to the Church.
Further, the chapters on giving in 2 Cor. 8 and 9, where Paul says it's not to be compulsory and that it involves equality—both giving and taking—show that there's a mindset different from tithing.
The only quotes addressing "should Christians tithe" in the 2nd century—leaving out the ones that sort of 'accidentally' mention it by quoting Scriptures with the word tithe in them—are:
He prohibited anger; and instead of the law enjoining the giving of tithes, told us to share all our possessions with the poor. (Irenaeus, Against Heresies IV:13:3)
And for this reason they [the Jews] had indeed the tithes of their goods consecrated to him, but those who have received liberty set aside all their possessions for the Lord’s purposes, bestowing joyfully and freely not the less valuable portions of their property, since they have the hope of better things; as that poor widow acted who cast all her living into the treasury of God. (ibid. IV:18:2)
The tithes of the fruits and of the flocks taught both piety towards the Deity and not covetously to grasp everything, but to share gifts of kindness with one’s neighbors. For it was from these, I reckon, and from the firstfruits that the priests were maintained. (Clement of Alexandria, Miscellanies II:18)
Pepin the Short restored tithing
to support monks
One history book I read said that tithes came back under the reign of Pepin the Short among the Franks in the 8th century. It was reintroduced to support the monks.
I don't remember which book I read that in, and I haven't followed it up due to the position of the New Testament and the early Christians being so clear.
There's a couple more quotes that I've put up on the Giving Quotes page. The idea seemed clear to the early Christians that we share everything together, not that we tithe. Collections were taken, say Justin and Tertullian, but they were completely free will. No mention of tithing is made. (Justin, First Apology 67; Tertullian, Apology 39).