Who were the the "Prophets of Zwickau"?

The “Zwickau prophets,” i.e., Nicholas Storch, Thomas Drechsel, and Mark Stübner, etc., claimed to be prophets of God and to have received revelations directly from God. They were leading an anti-Protestant, anti-Catholic, spiritualistic attempt at communism and anarchy based on a view of taking the millennium by force as prophets. Thomas Münzer (1490–1525) was a radical figure in the Reformation who became a leader in the Peasants’ Revolt of 1524–1525. From this man we get a clear window into all of his associates:

Thomas Muenzer, one of the Zwickau Prophets, and an eloquent demagogue, was the apostle and travelling evangelist of the social revolution, and a forerunner of modern socialism, communism, and anarchism. He presents a remarkable compound of the discordant elements of radicalism and mysticism. (HISTORY OF THE CHRISTIAN CHURCH, PHILIP SCHAFF (Vol 7, Ch4, P75)

He started by being influenced by doctrines of the reformation but quickly became an extremist who was deposed from his church. He hated Luther even worse then the Pope even though before his ‘fall’ he was actually selected by Luther to become a Lutheran pastor in the city of Zwickau.

He was at enmity with the whole existing order of society, and imagined himself the divinely inspired prophet of a new dispensation, a sort of communistic millennium, in which there should be no priests, no princes, no nobles, and no private property, but complete democratic equality. He inflamed the people in fiery harangues from the pulpit, and in printed tracts to open rebellion against their spiritual and secular rulers. He signed himself “Muenzer with the hammer,” and “with the sword of Gideon.” He advised the killing of all the ungodly. They had no right to live. Christ brought the sword, not peace upon earth. “Look not,” he said, “on the sorrow of the ungodly; let not your sword grow cold from blood; strike hard upon the anvil of Nimrod [the princes]; cast his tower to the ground, because the day is yours.” (HISTORY OF THE CHRISTIAN CHURCH, PHILIP SCHAFF (Vol 7, Ch4, P75)

Although it might not seem that these prophets had any influence on the Christian world, Karl Marx did refer to Thomas Münzer in his own writings, so you could say they had an impact on the world's continued opposition to the church. The beliefs of the Zwickau Prophets goes back to a pre-reformation sect in Bohemia who held a, ‘Taborite creed’. Tabor was a city in Bohemia that held control of local gold mines, the citizens joined local peasants to develop a communist-like society. The key to their quasi-religious communits movement was in their view of the millennial reign of Christ. Taborites lived announced in the millennium there would be no more servants and masters. They promised people would return to a state of pristine innocence.

Zwickau, however, was near the Bohemian border, and there Müntzer was converted by the weaver and adept Niklas Storch, who had lived in Bohemia, to the old Taborite creed: in particular, continuing personal divine revelation to the prophet of the cult, and the necessity for the Elect to seize power and impose a society of theocratic communism by brutal force of arms. In addition, there was to be communism of women: marriage was to be prohibited, and each man was to be able to have any woman at will. Thomas Müntzer now claimed to be the divinely chosen prophet, destined to wage a war of blood and extermination by the Elect against the sinners. Müntzer claimed that the "living Christ" had permanently entered his own soul. Endowed thereby with perfect insight into the divine will, he asserted himself to be uniquely qualified to fulfill the divine mission. He even spoke of himself as "becoming God." Having graduated from the world of learning, Müntzer was now ready for the world of action. (Karl Marx as Religious Eschatologist, Mises Daily: Friday, October 09, 2009 by Murray N. Rothbard)

Although the influence on communism can be traced, there does not seem to be any lasting influence on Christianity. There is a link between the Bohemian movements and a Christian movement called the Hussites under a Czech reformer Jan Hus (c. 1369–1415) and there are some modern churches who think of themselves to be related to those movements, in particular the Moravian Church, Unity of the Brethren, and the refounded Czechoslovak Hussite churches. However these churches do not resemble the ideas of Thomas Müntzer at all so it seems the lasting impact is more related to the communistic side of things only.