Anabaptists (Greek ανα (again, twice) +βαπτιζω (baptize), thus "re-baptizers") are Protestant Christians of the Radical Reformation of 16th-century Europe, although some consider Anabaptism to be a distinct movement from Protestantism. The Amish, Hutterites, and Mennonites are direct descendants of the movement.
The name Anabaptist is derived from the Latin term anabaptista, or "one who baptizes over again." This name was given them in reference to the practice of re-baptizing converts who already had been baptized as infants. Anabaptists required that baptismal candidates be able to make their own confessions of faith and so rejected baptism to infants. The early Anabaptists disliked the name Anabaptist, claiming that since infant baptism was null and void, re-baptism was in fact the first baptism for them. Balthasar Hübmaier wrote: I have never taught Anabaptism. ... But the right baptism of Christ, which is preceded by teaching and oral confession of faith, I teach, and say that infant baptism is a robbery of the right baptism of Christ ...
As a result of re-baptism, Anabaptists were heavily persecuted during the 16th century and into the 17th by both Protestants and Roman Catholics.
While most Anabaptists adhered to a literal interpretation of the Sermon on the Mount which precluded taking oaths, participating in military actions, and participating in civil government, some who practiced re-baptism felt contrariwise. They were thus technically Anabaptists, even though conservative Amish, Mennonites, and Hutterites and some historians tend to consider them as outside of true Anabaptism. Conrad Grebel wrote in a letter to Thomas Müntzer in 1524: True Christian believers are sheep among wolves, sheep for the slaughter ... Neither do they use worldly sword or war, since all killing has ceased with them ...
Source: Wikipedia, "Anabaptist", available under the CC-BY-SA License.