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Rather than give you an exhaustive account of battle success or failure or talk about tactics and the like, I'm going to relate a specific story about Washington after the war that I've always found to be more indicative of how he was viewed by his soldiers than any of the other stuff.
The event in question is now known as "The Newburgh Conspiracy."
Put yourself into the rotten shoes of a Continental soldier in 1783. The war against Great Britain has been a pursuit of seven long years. You're likely to have served one or more full terms of service; you've poured blood and sweat into the soil of what you hope someday to be a country of its own. You've toed the line against British regulars, endured winter hardships and summer shortages. You've marched up and down the coast often without shoes or a good coat. You've aged. Your family has aged. You've lost friends and have shared a tent with disease and famine. Death is your oldest marching companion.
You like to believe that you've done this with a kind suffering courage, without word of complaint or notion of disobedience.
But while physical hardship is something to be expected, hardship incurred by the indifference of distant leaders or the unqualified expectations of those who live in insolent wealth and lift not a finger in service to this project. In order to pay you, these idle councilors haggle with paymasters and quibble over supply, find any reason, true or invented, to deprive you of what you've earned. You have indebted yourself and your family, even while in service, and promised pay is months in arrears, if not years. Another step would ruin you forever.
The congress and other elites seem to treat these issues with coldness and severity. In the absence of pay, at the very least, you could be offered a small amount of gratitude.
In camp, with little to do as the war winds down, you find that these harbored grievances are shared by a number of other soldiers, and amazingly, they are shared even by officers! Not only that, but some seem to argue that the continued wordless forbearance would be an irredeemable mark of shame. That bearing these burdens would be proof that you richly deserve the chains you broke when you volunteered to serve. These officers are encouraging action as demonstration of the gallantry which won a country.
What was the war if not a fight against tyranny? What kind of soldiers would exchange one collar for another? Tyranny can and will wear the plain coat of republicanism as well as the splendid robe of royalty, and one must know to recognize it in all its disguises.
What was the worth of all of this toil, this backbreaking labor for liberty, if the result is to starve and be forgotten?
What do you ask for now but justice? Gratitude and a place in posterity, elbow to elbow in history as on the field of battle?
This could have been the emotional state of a great many men in 1783. The war had been long, and shockingly brutal in some phases and in some places. Congress had had a bear of a time paying for anything, and those men who made an earnest effort to pay and support the army, understanding the grim need to keep soldiers fed, fit, and motivated - like John Adams - are often eclipsed by those who find that the army can support itself while they concentrate on other matters.
Officers especially felt the pinch. Or, at least, we know that quite a few did as they're the ones who left the record. In March of 1783, a letter began circulating the camp at Newburgh, New York, articulating the concerns imagined above (all quotes in italics are taken directly or paraphrased from the first letter). Partly prompted by the failure of congress to regularly pay them or their men, the waffling over the question of pensions for officers, many of whom have served faithfully for years now, and the stoppages of pay with the promise of being made up later are starting to fall on deaf ears.
A number of highly regarded men cosign, or at least support, this letter. With the benefit of the historical gaze we know that the author was likely John Armstrong, Jr. (who would be appointed Secretary of War during the War of 1812). Henry Knox (another future SecWar) was also prominent in debates and public statements of support for fair pay and for post-war pensions.
There was, in short, a great deal of unrest among very prominent men.
The letter was of particular concern to Washington. Initially, he thought that the letter was a work of conspirators outside of camp, which was a fear that he and other federalists would later echo during times of public crisis: the poles of politics of that era were the anarchy of "the mob" and the tyranny of centralized power. The danger or reality of both was at times greatly exaggerated, but nevertheless there are numerous examples of federal overreach or dangerous mob actions.
To a man like Washington, this had the potential of spinning the republic out of control. A letter like this was just the kind of demonstrative sedition that could cause a general mutiny that could only be corrected through bloodshed.
Washington quickly moved to quash this insubordination, and called for a meeting. [see /u/MrGrumpyBear's correction below]
Now put yourself into Washington's shoes. He has shirked no discomfort, made no complaint, expected his men endure no hardship that he himself was not willing to cheerfully share. He has never left their side one moment He has suffered the stabbing cold at Valley Forge, and worse winters besides; he has smelled the powder smoke and staunched the blood of battle; he has suffered insult and indignity in the press, has laid his reputation, future, property, and life on the line no less than any man of the line. He considers his own military reputation as inseparably connected with that of the army.
Through it all, his genius has not been to spank the British up and down the coast, it has been to keep the army whole through hardship and embarrassment and reversal. At the end of the first terrible campaign season, when his army threatened to splinter into oblivion before his eyes, he kept a core together through a harsh, starving winter. He has prevented mass desertions after entire seasons of retreat, retreat, retreat, eking out his victories by blunt force of character, rather than subtlety of tactics or elegance of maneuver.
That his army would melt away not from British grapeshot, but from internal politicking, at the eve of victory, was utterly unthinkable. How subversive of all order and discipline.
He writes a reply, written with the same kind of great art that was evident in the anonymous circulation, that advises honor, dignity, and patience, all virtues previously shown by the army in all of their shared privations, for is this army not celebrated thro' all Europe for its fortitude and patriotism?
But what alternative is proposed by this insidious foe who drafted the letter? For he must be a foe, for who but a foe would council turning our arms against our country in the extremest hour of her distress? He cautions mere reflection; and on reflection, the repudiation of the ends sought by malefactors.
By thus determining — & thus acting, you will pursue the plain & direct road to the attainment of your wishes. You will defeat the insidious designs of our enemies, who are compelled to resort from open force to secret artifice. You will give one more distinguished proof of unexampled patriotism & patient virtue, rising superior to the pressure of the most complicated sufferings; — And you will, by the dignity of your conduct, afford occasion for posterity to say, when speaking of the glorious example you have exhibited to mankind, had this day been wanting, the world has never seen the last stage of perfection to which human nature is capable of attaining.
As Washington finished his address, he was unsure what effect, if any, it had had on the assembled officers. To prove that measures were being taken to address the grievances brought up by the letter, even as irregular and improper they were, he produced a letter from Joseph Jones, a colleague in congress, outlining proposals in support of the army.
Jones wrote, apparently, with a neat, tight hand, and Washington's vision had begun to fail.
As you watch Washington give the address, he must have been every inch the general of your experience. A large, imposing man, not often given to displays of passion, had just fired volleys of condemnation upon the secret architects of the original letter. It was true that Washington had been the tentpole of the army, a reliable figure in and out of camp. Tireless and a legendary even before the war had ended.
What do you feel now? Shame? Perhaps. A certain reluctance to fully engage in what before had seemed so clear and close - you do deserve recognition, gratitude, and support, but to take it by force? Was that ever a real possibility?
As Washington ends the speech, he pulls out a letter. And suddenly that tireless engine that drove the continental army to victory against the greatest army on earth looks tired. Old. Worn.
He squints at the letter. Looks up at the assembled men, almost sheepishly, and pulls out a pair of spectacles. Raising them to his nose, he says, quietly, "Gentleman, you must pardon me, for I have not only grown gray but almost blind in service to my country."
Continued below
/u/PartyMoses gave a really great answer, but I wanted to add a little more about Washington's military abilities.
Washington was no Napoleon, certainly. He had no great open-field victories, and his greatest success was the Siege of Yorktown, a battle won more by logistics and training than by tactical brilliance and dramatic maneuvers. Still, in the grand scheme of things, I would rate Washington as a very good general totally separate from the personal gravitas PartyMoses described.
Washington's greatest strength as a commander-in-chief is that he was pretty good at delegating, and was an EXCELLENT talent scout. The Continental Army suffered from an inconsistent officer corps throughout the war: officers were often petty, fickle blowhards who would resign their commissions, duel each other, or blow off their responsibilities with little provocation. From the earliest days of the war, Washington began building a cadre of officers that were both fantastic at their jobs and personally loyal to him. Henry Knox was the first Washington adoptee, as his transport of a "noble train of artillery" from the captured British cache at Fort Ticonderoga to Boston during the winter of 1776 proved him a man of ability, ingenuity, and dedication. Knox eventually rose to Major General and chief of artillery, and the artillery corps he built was one of the best parts of the army. Knox's artillerists swept the Hessians from the streets of Trenton, broke the British charge at Monmouth, turned the Hudson River into a death trap in the forts around West Point, and performed so well at Yorktown that they drew commendation from British and French officers. Next came Hamilton, Washington's chief-of-staff and political hatchetman. The little shit had a huge ego and even larger ambitions, but he knew how to write and could dive into the political muck in ways Washington couldn't without ruining his image. Hamilton made sure Washington's enemies in the army and in Congress remained isolated and unpopular, saving his boss' job even in the low years of 1776-1778. Washington named Von Steuben Inspector General (drillmaster) of the army, replacing an obnoxious political foe, Thomas Conway, with a capable officer who drilled discipline and real proficiency into the army. Lafayette, Greene, and Morgan round out this list of Washington favorites as talented fighting generals. Greene was something of a double threat; Washington pulled him from a combat command during the winter at Valley Forge and made him Quartermaster General, where he devised a system of confiscating supplies the army needed to survive from local farmers with a smile and an IOU. This system allowed the army to operate at at least subsistence levels without alienating the general public.
Washington also had the foresight to see the latter half of the war as a "war of posts," a conflict decided by control of strongpoints that would either force the enemy into a frontal assault or drag the war on until it lost all popularity in the British government. From 1778 until 1783, Washington played a careful game of cat and mouse with the British, keeping them hemmed into New York City, northern New Jersey, and Westchester county without actually ever giving them a real battle. A less disciplined commander may have gotten bored or caved to pressure to get a win and done something stupid. The British did this, overextending themselves at Stony Point on the Hudson River (and, in the Southern theater, at Cowpens and King's Mountain, though Washington had nothing to do with either of those), where an isolated forward position was knocked out by American light infantry. Washington succeeded in playing a very cool long game, and it proved to be a winning strategy.
When Washington DID move, he could do so with surprising alacrity. His winter offensive against Trenton and Princeton in 1776-early 1777 saw him surprise one enemy position, outmaneuver a British relief force, and strike a second outpost. Those these battles were not large, they did cause the British to evacuate New Jersey. The frustration of seeing the British army willingly give up so much territory for such minor defeats, and the brutal Patriot retaliations against those that had outed themselves as friends of the Crown, did permanent damage to the open Loyalist support the British would have needed to hold territory during the war. Washington's sprint down to Yorktown with the French caught the British high command in New York completely by surprise; by the time British commander-in-chief Sir Henry Clinton realized that the allied armies' objective was Cornwallis' army and not British headquarters in Manhattan, Washington was already halfway across New Jersey.
While Washington suffered some horrible losses - Long Island, Brandywine, and Germantown almost ruined his career - the commanders, strategies, and maneuvers that won the war all came from him.
Sources
Wayne K. Bodle, The Valley Forge Winter
David Hackett Fisher, Washington's Crossing
Martin and Lender, A Respectable Army
Lender and Stone, Fatal Sunday
While waiting for answers you might like to check out Was George Washington really a brilliant strategist? with a comment from /u/Sluggian, which draws from The American Way of War: A History of United States Military Strategy and Policy by Russel Weigley, and What were George Washington's strengths as a military commander and how did he rate among his peers of the time? with a comment from /u/KingWalnut, which draws from the biography Washington: A Life by Ron Chernow.
Washington was maybe more logistician than tactician, although an argument could be had that logistics were what his particular war required. A good example of his usefulness at the strategic level would be his role in inoculating his army against smallpox. A major smallpox epidemic ran concurrent with the American Revolution—I cannot recall exactly where it started, but Elizabeth Fenn in Pox Americana does a good job tracing the outbreak of disease, which spread through the Native American population and throughout the eastern seaboard, and also out west and into Mexico and Alaska—her detective work in tracing the disease through populations that left little written record is pretty good. Washington had some experience with disease (not a lot, mind you! but my memory is that he had smallpox some decades earlier in ... I just checked, wanted to say Jamaica, but it was Barbados), and some knowledge that inoculation could prevent outbreaks in his army. He made the decision (against some popular sentiment) to have his troops inoculated, a decision that diminished the advantages of the British (among whose troops immunity to smallpox tended be more widespread) and (Fenn argues) contributed to safeguarding the Revolutionary Army against destruction by smallpox. It's tempting to point to one decision as being critical—but that sort of preparedness and care in preserving the existence of his army was kind of Washington's thing, and, I'd say, the aspect at generalhood that he did well.
Fenn, Elizabeth. Pox Americana: The Great Smallpox Epidemic of 1775-82. 2002.
A simple but important correction to the otherwise laudable comprehensive responses that have been posted herein regarding the Newburgh Conspiracy:
Though the events in question are referred to as The Newburgh Conspiracy, the Continental Army encampment where Washington's remarkable speech took place was not in Newburgh. Washington's headquarters was in Newburgh, while the encampment and other officers' headquarters were a few short miles away in New Windsor, NY.
New Windsor Cantonment, the Last Encampment of the Continental Army, and Washington's, Knox's and Gates's headquarters are all state or local historic sites open to the public. The Cantonment includes a replica of the temple hall in which said historic culminating events took place. All are well worth visiting.
New Windsor Cantonment (Also the home of the National Purple Heart Hall of Honor. Additionally, The Last Encampment of the Continental Army is a town park across the street comprising additional acreage of the sprawling original camp and some replica structures.)
Washington's Headquarters (The grounds include a museum separate from the headquarters house itself)
Knox's Headquarters (This house also served as Gates's headquarters)