The importance of each war or historical event is always in the eyes of the beholder. For me it was the conflict in Vietnam because it is the first time we actually withdrew, and it was because of so many Americans rising in protest of something they knew little about. Then we promised air support to the South Vietnamese if the North broke the treaty, then when they did, and because of a president afraid of the American people, Gerald Ford, we failed to deliver causing the death of thousands of South Vietnamese and the loss of American POWs. This was a war that all the soldiers knew they could easily win and end, but because of politics they were not allowed to do so. It was a war not won because of American civilians. Instead we withdrew, leaving the defense of South Vietnam to the ARVNs. What is a shame is that those soldiers are looked down upon to this day, while those in Iraq and Afghanistan are treated as heroes, even though there are many more atrocities being committed now, than there ever was then. To me it is a shame to have treated those young men (the youngest and most educated ever) in the manner they were and are treated.

In order of importance to our country:

Revolutionary War - gained our independence

Civil War - Because the South fought against unfair taxes and tariffs (Slaves were held by both the South and North, but only six percent of Southerners were slave owners. Do you really think the other 94% fought for the rich slave owners? It was because the South legally (according to American laws) seceded from the union in protest of those taxes and tariffs. The ware began when the Union Army invaded the South. Case in point is that Robert E. Lee freed all his slaves before the war, while Ulysses S. Gant did not free his until after the war when it was mandated by law. At that time the Northern factories had to free their slaves; they were replaced by child labor.

Vietnam War - Americans for the first time failed to support their troops

WWI and WWII - In both it was a fight against world domination

Korean War - Spanish American War - Cold War - All others

Definitely the Revolutionary War, if we hadn't won we wouldn't be asking this question instead it would be "What is the most important moment in the history of the British Colonies?"

After that I would say that the Civil War would be the next most important, followed by World War II and then World War I.

I'm not sure there is any objective way to answer this question. Even if there was, it would be impossible to consider all the involved variables. It is very possible that the most important event is something which no one considers important - a life or a death that went entirely unnoticed.
For example, during the American Civil War Thomas 'Stonewall' Jackson was mortally injured and died. He is considered by many to have been one of the great military geniuses of his day - on the same level with or perhaps even superior to Robert E. Lee. Many ponder if Jackson had survived and been present at the Battle of Gettysburg whether Lee might have won the battle and we might still exist as two separate nations - the Union and the Confederacy.
Similarly, we see a "nobody" shoemaker who teaches a Sunday School class converts D.L. Moody to the Christian faith and Moody becomes one of the most outstanding evangelists in modern history.

"The declaration of independence"
I think this is most important because it not only made America an independent nation also pave the way to independence for other nations who were under the British rule. This incident make them the most influential nation and till now they are like that.

The Signing of the Declaration of Independence.

Monday, August 6, 1945, with the dropping of the first Atomic bomb over the city of Hiroshima, Japan.
This event changed forever the path that humanity will follow toward its survival or its destruction.
In my opinion no single moment in American history up until that point has had the far reaching effect that the action of the USA created on that day.

I dont know about that picture but I thinks every date is important in American history when they fight with other country.
One day America will get the result.