In ancient Greece, there were a number of competing philosophies, religions, and quasi-religious systems. One of the most famous were the Stoics, who felt that the highest good in life was achieved by having one's will aligned with Nature. Thus virtue was achieved, in some sense by doing one's duty irrespective of emotional attachments or feelings. Stoicism was a fairly noble belief system as far as non-Christian beliefs go, as it produced people who were often highly moral. But, Stoicism's inadequate moral foundations (i.e., there is no absolute standard of morality within it) resulted in its eventual collapse and eclipse by Christianity.
Despite that history, a certain form of Stoicism lives on in some ways within the Church that defeated it. I am thinking here of the kind of Christians and churches in which performance and adherence to a given standard are seen to be the markers of spiritual maturity. Thus, to the extent that a Christian reads his Bible, prays regularly, gives to the Church's needs, and keeps the moral code (which may be higher even than God's!), that person is seen as successfully living his/her Christian life, even if the reasons for doing all these things are little more than the meeting of religious obligations.
One usually sees the more extreme forms of this kind of "Christian Stoicism" within what I would call more "fundamentalist" churches, but it is a danger even for those of us who broadly identify with the "evangelical" label. How many of us, after all, have at least periods of our lives when we are simply "going through the motions" of godliness, doing our religious duty, avoiding all the "big sins" (on our self-defined list) and hiding all the little ones? If we're not careful, the joy our salvation can get replaced by this kind of desperate forced march to eternity, of doing good without really being good or even experiencing following Christ as good.
When that happens, we have replaced Christianity with Stoicism.