England underwent a period of instability and crises both at home and in the colonies during the 1700s. What might have happened in England and her North American colonies had the Glorious Revolution not taken place?

The Glorious Revolution of 1688 deposed King James II in favor of his daughter Mary and her husband, William. William and Mary were Protestants, whereas King James II was a Catholic and had just fathered a son that people feared would be raised Catholic. Further, James favored an authoritarian, absolutist vision of monarchy, much like that favored by Louis XIV in France. This was a model that the English people hated and rejected.
The Glorious Revolution led to an important document, the Bill of Rights of 1689. This document, based on the work of John Locke, gave more power to parliament and curtailed the power of the monarchy. Notably, it allowed citizens the right to dispose of an unjust monarch. The document became influential in ensuring Britain developed a constitutional monarchy, and it became a basis for the US Constitution. It also provided a rationale for the colonial revolt against King George III.
Without the Glorious Revolution, England could very well have gone in the direction of absolutist monarchies such as the Bourbons in France, concentrating power in the hands of the king. The 1689 Boston revolt against Edmund Andros, who was trying to curtail rights as well as impose the Church of England on the Puritans, probably would not have succeeded. Very likely, neither England nor the colonies would have developed the concepts of freedom and individual rights that led over time to prosperous and growing societies.
English society and the colonies would probably have looked more like France and Spain, with a tiny and wealthy class living in vast luxury while everyone else suffered. (There was some of this in England, but not to the degree of autocratic countries like France and Spain.) Rather than gradual evolution towards greater democracy and equality in Britain, when a revolt came, it would have most likely been a violent overthrow of the existing government, such as occurred in France, and the revolutionaries would have had few models for setting up democratic government.
One could argue that neither England nor her former American colonies would have become predominant world powers without the Glorious Revolution providing the pattern of a more representative, free, and equalitarian government. The Glorious Revolution did not usher in modern equalitarian government as we understand it all at once, but it was an important first step in that direction.