For many generations, most English colonists in North America were happy to be subjects of the British Crown. Even in the years leading to independence, many never dreamed of separating from the mother country. However, there were a number of changes in British policy beginning in the 1760s that finally pushed many to fight for independence.

After the French and Indian War, the British government started changing its overall policy towards the way it ran its colonies. Previously they had ruled with a rather hands-off approach. The powers in London were content to let the colonies essentially function on their own. The colonists, for their part, liked this arrangement. They saw themselves as free English subjects who were privileged to live in a land far enough away from London to conduct their lives as independent people but under the overall protection of the Crown.

However, after the French defeat in 1763, the British authorities felt that the colonists needed to pay their part for a conflict that was largely fought for their protection. For one thing, they instituted new taxes on the colonists. This was one grievance since these laws were being imposed on them by a Parliament in which they had no representation. Protests against these taxes led to harsh clampdowns and collective punishment. After the Boston Tea Party, for instance, the charter of Massachusetts was revoked and the port of Boston was closed.

As Britain tightened its grip on managing the increasing disgruntled colonies, posting garrisons in cities, imposing taxes, and limiting settlement, many colonists came to the understanding that their previous freedoms were slipping away. While calling the actions of the King and Parliament tyranny was mostly hyperbole, there were still real fears that if things continued down this road, they would lose more and more rights that they saw as naturally theirs as a free people. Consequently, it was this desire for control of their own dwindling domestic freedoms that compelled many colonists to part ways with Great Britain.

The revolutionary leaders who declared independence in 1776 did so for a number of reasons. One was that they believed they had passed the point where reconciliation with Great Britain was possible. The Revolutionary War was in its second year by 1776, and thousands of men had died in the conflict. By this point, a political resolution to the conflict seemed impossible. The King had rejected conciliatory petitions (including the so-called "Olive Branch" petition of the summer of 1775). So, while many revolutionary leaders did not desire independence at first, they were driven to that position by the pace of events.

Another reason why the colonists declared independence was the need to establish domestic governments. Most of the colonies were run by revolutionary councils or conventions, who ruled essentially under their own authority amid the emergency of the Revolution. In order to write constitutions to set up permanent governments, independence had to be declared.

Finally, there were geopolitical and diplomatic reasons for the colonies to declare independence. The revolutionaries desired French (and Spanish and Dutch) assistance in fighting the British, but the French in particular would not enter the conflict as long as it was essentially a dispute between colonies and mother country. Once independence was declared, American emissaries in Paris had the authority to negotiate a treaty of alliance with the French, whose assistance was vital to winning the war.

As an English teacher, I am going to answer this by providing a literary answer.  I teach 11th grade, and therein my classes watch and read the play/musical 1776.  If you can find a copy, I strongly suggest reading the appendix.  It provides a detailed breakdown of the facts and fabrications detailed within the play (those instances where they adhered faithfully to historical fact and those instances where they strayed--most importantly, they explain why).  Within the play it talks about the the mishandling of the colonies by the British crown, and how, in essence, the colonies (its people, resources, industry, etc) were used by the crown for its own benefit, but without receiving the rights, privileges, etc, common to any British subject.  There is a really good line where the character of Ben Franklin offers that he would not mind being referred to as an Englishman were he given the full rights of an Englishman.  Anyway, it is a wonderful resource that will allow you into the minds of these men and will bring history to life for you.  Below are some links for you.

Why did the colonies want to break away from Great Britain?

First, we should realize that not all the colonists wanted to break away from Great Britain. There were many who wanted to remain loyal to what they viewed as the mother country, and even many ardent patriots did not think of the Revolution as a movement for independence until the war itself. But to look for the reasons the colonists wanted independence, we can look at the Declaration of Independence itself. It asserted the colonists' claims that the British had violated their natural rights which in some cases coincided with their rights as British subjects. This included the policy of taxing the colonists without their consent, quartering troops among them, dissolving colonial legislatures, establishing courts outside the colonies to try violators of certain laws, and other offenses. There were also other, more pragmatic reasons for declaring independence not mentioned in this document. The colonists were, after all, at war with Great Britain, and they needed the support of France and other European powers. They could not get this help without declaring independence. They also needed to establish state governments since the royal governors had fled the colonies with the outbreak of the revolution, another issue that couldn't be addressed without declaring independence. Finally, more than a year of war had alienated the colonists and the British to the point where reconciliation seemed impossible. So in the words of Thomas Paine, it was "common sense" that the colonists should become independent.