both sides. Following the battle, Congress addressed the Olive Branch Petition to King George III, reaffirming loyalty to Great Britain and pleading with the King to intercede. Up to this point, many in the colonies blamed Parliament alone for the Crisis and felt that the King would protect them if he only knew the American side of the conflict. George III forever dispelled this hope when he issued the Proclamation of Rebellion on August 23rd, 1775. The King declared the colonies to be in open rebellion, labeled the Congress a "conspiracy of ill-designing men," and authorized the use of military force to end the rebellion. For many delegates, independence became inevitable at this point, as did a protracted war to achieve it.

2. Common Sense: What the Proclamation of Rebellion did for the delegates in the Second Continental Congress, Common Sense did for the common people. Published by Thomas Paine on January 10th, 1776, Common Sense was a treatise arguing for American independence from Great Britain and the establishment of a single American nation with an egalitarian government. Clear, concise, and powerfully written, Paine's message spread like wildfire throughout the colonies, encouraging those outside of Boston to make common cause with the Massachusetts militia.

3. The Evacuation of Boston: After Bunker Hill, the British stayed within Boston while George Washington, now in command, struggled to bring order and discipline to the volunteer force. Thus, neither side actively sought battle. This stalemate was broken when Colonel Henry Knox pulled off a logistical miracle, dragging the heavy cannons from Fort Ticonderoga in the wilderness of upstate New York over mountains, lakes, and rivers to Boston. Washington then, quickly and in great secrecy, had the cannons placed at Dorchester Heights. When British General William Howe saw that his fleet had moved within range of heavy guns overnight, he knew that his strategic position had become untenable. British barrages were unable to reach the Heights. Washington received word that the British would spare Boston if they could depart unmolested. On March 17th, Howe and his forces departed for Britain. The Evacuation of Boston was a crucial intersection between the military and political situations, similar to battles like Saratoga and Trenton. The British retreat was stunning, and it showed the colonies that military victory was possible.

4. The Lee Resolution: Richard Henry Lee of Virginia arrived at the Continental Congress on June 7th, 1776, with new instructions from his home-state of Virginia. Convinced by the victory at Boston that the Revolution could be won, leaders in Virginia authorized Lee to propose the following resolution:

Resolved, That these United Colonies are, and of right ought to be, free and independent States, that they are absolved from all allegiance to the British Crown, and that all political connection between them and the State of Great Britain is, and ought to be, totally dissolved.

This was a crucial moment in the drive for independence within Congress. Up until this point, Massachusetts had been the driver of events, and it was crucial that the other colonies also take a stand. Virginia, as the most populous colony, was the natural leader of a nation-wide independence movement. In fact, it was, in part, because of Virginia's prominence that George Washington had been named the leader of the Continental Army.

5. The Declaration: The Lee Resolution produced a furious floor debate between moderates and revolutionaries. Despite the Proclamation of Rebellion, many in the colonies were not yet resolved to breaking with Great Britain. The wealthiest colonies in particular—New York, South Carolina and Pennsylvania—were unwilling to risk the damage to trade and property that a war of independence threatened. Making matters harder, John Adams and the other leaders of the faction for independence recognized that the Lee Resolution must be passed without opposition, or not at all. On June 11th, the debate ended, and a final vote was scheduled for July 1st. A committee was also formed to draft the Declaration of Independence, should the motion carry. Slowly, after seeking support from home, the delegates privately assured Adams of their colony's support until only New York, Pennsylvania, Delaware, and South Carolina remained in opposition. At the same time, Jefferson worked on the declaration, drawing upon rhetoric he had used many times before in other documents and pamphlets. South Carolina was finally persuaded. Caesar Rodney rejoined Congress to push Delaware into the independence column. The most recalcitrant delegates from Pennsylvania, recognizing they were outnumbered, agreed to absent themselves from the final vote. New York, meanwhile, facing a massing invasion force on Staten Island, promised to abstain from the vote provided there was no opposition. On July 2nd, the Lee Resolution was carried 12-0. On July 4th, independence was formally declared and the final version of the Declaration of Independence was published and read aloud throughout the colonies. The United States of America had its independence—if it could win it.

Aftermath: In military terms, the remainder of 1776 was a disaster. Washington was unable to prevent the British landings at Brooklyn and Manhattan. His forces were then driven from New York City, defeated at Fort Washington and White Plains, and chased all the way to Pennsylvania. The Declaration of Independence seemed like a hollow gesture in the face of such failure. As December 1776 neared its close, Washington faced the disintegration of his army as enlistments were nearly up for many soldiers.

In the face of this nadir, Thomas Paine again took up his pen and published The American Crisis, which successfully rallied public opinion and the attitudes of many soldiers to continue the fight. In order for this new resolve to be sustained, however, Washington needed a victory. Thus, on Christmas night in 1776, the American commander famously led his troops across the icy Delaware River and launched a successful dawn attack on the Hessian troops at Trenton. This victory was followed up by another surprise attack at Princeton. Washington's dauntlessness convinced the army, the colonies, and the world at large that the cause was still alive.

1776 focuses primarily on military events because the author covered political events of the same year in a previous book: John Adams.

The first important event described in the war actually took place in October 1775, in London. King George III gave an important speech to British Parliament in which he promised to crush the rebellion. After that speech, peaceful reconciliation was out of the question.

The second key event happened in March 1776. The Americans put cannons in Dorchester Heights, forcing the British to evacuate Boston. Henry Knox, head of artillery, had dragged the cannons 300 miles from Ticonderoga to Boston.

The third major event, which the author describes as the most important event in the book, was George Washington's escape from Brooklyn in August. Despite being defeated in battle, Washington managed to extricate his weakened army. Had the British managed to trap Washington, the war would have been over.

A fourth significant event was at the end of 1776. The British drove Washington's depleted forces across New Jersey. With Washington on the verge of defeat, the British went into winter quarters. This enabled the Americans to rally and win victories in the Trenton-Princeton campaign. For the second time, the British had allowed Washington to recover and escape.

A final event that unfolded gradually throughout the year was George Washington's development as a field commander. He learned from the mistakes he made and became much more decisive and capable in subsequent years.

These are the five most significant events in 1776.

It is, of course, difficult to point to exclusively non-military events in a book that focuses so much on the Revolutionary War. So there are some events in this answer that are basically military. Still, some are more political in nature. 

The first event actually occurs in October of 1775. After a speech by King George and a lengthy debate in Parliament, with significant dissenting voices, both houses of Parliament voted to approve Lord North's plan to send a large military and naval force to the colonies, then in a state of all-out rebellion. This marked, in many ways, a point of no return in the conflict and was thus a major event. Another occurred in March of 1776, when Washington's capture and fortification of Dorchester Heights forced the British army to abandon the city of Boston. McCullough describes this event as the "first thrilling news of the war" for the rebels (108). 

Another event, of course, was the decision of the Second Continental Congress to declare independence from Great Britain. This decision, reached on July 2, meant that the war would be an "all-out war for an independent America" and was a major turning point described in the book (137). But this occurred even as another crucial event was taking place--the massive invasion of New York by the British army and navy. Finally, the book closes with a speech by King George in 1777. Echoing the debates in Parliament at the beginning of the book, the speech announced that, despite the previous year's events, the Americans had not "recovered from their delusion" (292).