Recently, I attended a mainline church here in St. Louis and heard the children’s sermon in which the children were instructed that the cross showed us how much God loved us, and that Jesus shows us the right way to live. Nothing else was said: nothing about the atonement, nothing about what Jesus was doing there (except a possible inference that He was somehow setting an example of self-sacrifice) and certainly nothing about how we actually go about being like Jesus apart from emulating a certain niceness which is desired of all Christian boys and girls.
Louis Berkhof has something to say about this in his Systematic Theology (pg.387-388). He speaks directly to the Example Theory of the Atonement.
This theory was advocated by the Socinians in the sixteenth century, in opposition to the doctrine of the Reformers, that Christ vicariously atoned for the sin of mankind. Its fundamental principle is, that there is no retributive justice in God which requires absolutely and inexorably that sin be punished. His justice does not prevent him from pardoning whom He will without demanding any satisfaction. The death of Christ did not atone for sin, neither did it move God to pardon sin. Christ saves men by revealing to them the way of faith and obedience as the way of eternal life, by giving them an example of true obedience both in His life and in His death, and by inspiring them to lead a similar life. This view really establishes no direct connection between the death of Christ and the salvation of siners. Yet it holds that the death of Christ may be said to expiate the sins of man in view of the fact that Christ, as a reward for His obedience unto death, received power to bestow eternal life on believers. This theory is objectionable for various reasons.