Non-denominational History
Non-denominational Christian churches are almost exclusively derived from the Protestant movement, as a fundamental part of Catholicism is visible organizational unity Ecclesia militans or the body of the Church consisting of living members.  This is not to say that the visible unity of the Church was not an important doctrine of the Protestant Reformation. The Reformers of the 16th century Magisterial Reformation believed that they were reforming the Church Catholic. Each of them took very seriously the charges of schism and innovation, denying these charges and maintaining that it was the medieval church that had left them. Because of this the fundamental Unity of the Church Catholic remained a very important doctrine in the churches of the Reformation. Dr. James Walker wrote in "The Theology of Theologians of Scotland": 

The visible church, in the idea of the Scottish theologians, is Catholic. You have not an indefinite number of Parochial, or Congregational, or National churches, constituting, as it were, so many ecclesiastical individualities, but one great spiritual republic, of which these various organizations form a part. The visible church is not a genus, so to speak, with so many species under it. It is thus you may think of the State, but the visible church is a totem integral, it is an empire. The churches of the various nationalities constitute the provinces of this empire; and though they are so far independent of each other, yet they are so one, that membership in one is membership in all, and separation from one is separation from all... This conception of the church, of which, in at least some aspects, we have practically so much lost sight, had a firm hold of the Scottish theologians of the seventeenth century.

Wherever the Protestant Reformation took place, the founders claimed that the result was not a new denomination but a reformation of a supposedly pre-existing "national" church.  Denominationalism was accelerated in the aftermath of the Westminster Assembly convened by the English Parliament to formulate a form of religion for the national churches of England and Scotland. In the debate between the two main parties present at the Assembly, the Presbyterians and the Independents, the Presbyterians were in favor of a form of church government that maintained the visible organizational unity of the Church Catholic while independents, weary of the ecclesiastical tyranny they experienced under the Episcopal system, wished to organize the churches in a congregational way envisioning no legitimate authority of the church above the local congregation meeting at one time in a single place. Obviously these two parties were not reconciled and following the Assembly the Independents formed their own independent church. Thus instead of a united expression of the Church Catholic in England there were now two churches.  Protestant Denominations spread and multiplied especially in the United States as Denominational confessional statements began to be used more to exclude than to include Christians with different doctrinal convictions. Each denomination maintains to differing degrees some form of organizational and visible unity with its member churches, albeit radically decentralized compared with the Catholic Church. Today, non-denominational churches, like the Independents at the Westminster Assembly, refuse to recognize any ecclesiastical authority above the local congregation and deny the visible unity of the Church (though not the unity of the invisible Church despite the fact that the original denominations were formed by substantially the same ideology.  In the United States, the number of evangelical non-denominational churches often included in the category of American Protestantism has increased exponentially since the late 1950s Many historians of American religion cite after-effects of the Scopes Trial and baby boomers, as well as the higher standard of living available in the United States, and the movement away from authority in American culture due to Watergate and other scandals.  Other reasons of growth may include an increase want to focus on Jesus. Some people feel that belonging to a Christian denomination can pull focus off Christ and onto certain principles of the particular denomination which are not Christ. So growth may be caused by Christians which literally means "partisans of Christ of the household of Christ, who want to focus on Christ Jesus rather than denomination principles.  Non-denominational churches range from only few members to "super" or "mega" churches of congregations of 1500+ attendees.