What role did the Protestant Reformation play in the colonization of North America?
As rrteacher stated, the Protestant Reformation led to the stratification of western Christianity. Throughout the Middle Ages, there were numerous conflicts, but the Catholic Church acted as a sort of permanent "referee" and intermediary, since all Christian nations in the West submitted (at least nominally) to the authority of the Church. The Protestant Reformation ended that era. Protestants no longer acknowledged the authority of the Church, and individual Protestant sects did not acknowledge the authority of any other sect. This led, as mentioned elsewhere, to New World settlement as an escape from persecutions by Catholics or other Protestants.
One could also argue that the Protestant Reformation was an important prerequisite to colonization of North America due to the Treaty of Tordesillas. The Treaty of Tordesillas refers to a series of agreements, mediated by the Pope, which essentially divided the right to colonize the world between Spain (in the West) and Portugal (in the East). England was not a party to this agreement, so the English may have run afoul of the Pope if they had remained Catholic and attempted to settle in lands claimed by Spain. However, England converted to Protestantism, which caused them to view their New World conflicts with Spain as conflicts with a hostile and heretical opponent, rather than as a quarrel among family members.
The Protestant Reformation led to the creation of a number of splinter groups who became religious minorities in their respective lands. This led to social unrest and turmoil, as many of the minorities were persecuted. North America began to be perceived by many in Europe as a "safety valve" for religious dissenters, notably French Huguenots. Obviously, the Puritan experiment in New England was begun by dissenters who hoped to establish a society on their own terms, but many other colonies established varying degrees of religious tolerance in an effort to attract settlers. Puritans flocked to other colonies, notably Bermuda, but Huguenots were welcomed in Carolina, New Amsterdam/New York, and other colonies. Quakers, persecuted in New England as well as their home country, found a haven in Pennsylvania, established by proprietor William Penn, himself a Quaker. Religious dissenters also went from one colony to another in search of religious freedom, with Rhode Island, Pennsylvania and North Carolina being particularly desirable destinations. Later in the eighteenth century, additional religious dissenters came from Europe, including German Moravians, Mennonites, and other sects. The primary motive for settlement of North America was undoubtedly economic, but religious motives were a factor for significant minorities of settlers.