I took a class on this recently (most of our info was from James L. Stokesbury's a short history of the civil war and lectures), and essentially it boiled down to a combination of things. Firstly, there was a significant gap between killing capability and firing tactics. Line firing was the norm, but the use of minee balls, rifling, and (later on) repeating rifles meant that very high casualties were the norm. Secondly, as stated before, often it is said that over *620,000 Americans died in the war, and while technically true from a union perspective (the confederacy was never recognized as an actual country by the U.S.but rather as U.S. territory occupied by citizens in rebellion), it is likely counted as a sum total b/c the Confederate dead, missing and wounded, after the dissipation of the confederacy were now the responsibility and burden of the union and had a huge effect on the Southern U.S. The last factor I can think of that contributed to very high casualties is disease. Without understanding of sanitation and infection and proper medical care, huge numbers of wounded soldiers ended up dead or with amputations or were otherwise incapacitated. I don't know if it was as big a problem on European battlefields; maybe the rural/undeveloped land and sparsely settled nature of the theaters in which the war was fought meant a lack of proper medical facilities or infrastructure needed to facilitate mass medical care? Not sure on that one. I'm sure there are other reasons, but these are the three that were brought up the most for me.

EDIT: 620,000 deaths from the Civil War, I was thinking of a totally different statistic

When you say US deaths, do you mean Union, Confederate, or combined? It's not uncommon for informal American Civil War casualty figures to simply total them up and say "This many Americans were killed" rather than "X Union and Y Confederates were killed".

Well, for one, it was a civil war. Every person that died was an American. For comparison, the English civil war was the most devastating war to England on a per capita basis. The next contributing factor was that military tactics did not suit that level of military technology. For instance, this is one of the first wars in which the cavalry charge becomes worthless. In wars prior to this cavalry troops acted as shock troops and to chase down a defeated army. If cavalry did that in this war, it would be torn to ribbons. In fact, cavalry would be used more for raiding and transporting troops than it would be for actual combat. Our as general Nathan Bedford Forrest is often misquoted as saying, getting to the battle the "firstest with the mostest." This lack of cavalry as the finishing stroke served to preserve defeated armies and prolong the war. Traditional use of line infantry was useless, add was seen at the battle of bull run and pickett's charge, in which marching lines were utterly decimated by rifle fire. That doesn't mean they didn't try though, and tens of thousands died because of this. In my opinion, the tactics and strategy used by the civil war armies look remarkably similar to early ww1 tactics. Hell, trench warfare was pioneered at Petersburg in 65. Something else I think doesn't get mentioned often enough is the way America conscripts it's population. It had only been relatively recent in Europe that most of the countries moved away from the professional army model. That had never been an issue in America, since we weren't afraid of giving our citizens guns. During this war, these armies were some of the biggest in the world. When you combine the size of the armies, the military technology, tactics, and the fact that everyone dead was an American, it shouldn't be too surprising the casualties were so high.

I hope it doesn't bother you if I point out that the premise of your question is slightly off. You are comparing American deaths in WWI, WWII, etc., to American deaths in the American Civil War, and, noting that American deaths were higher in this war than those other three combined, why the death count was higher in this war than the others (asking why the deaths were so much higher in this case). But those other three wars each resulted in far more deaths than the American Civil War (less than a million people died in the American Civil War, were as about 10 million died in WW1, 50+ million in WW2, and about 1.5 million in the Vietnam War). In fact, there were single battles in the Second World War (the Battle of Berlin, the Battle of Stalingrad, the Siege of Leningrad) that resulted in more deaths than the four years of the American Civil War.

The question really is why so few American died in these other wars compared to other nationalities, such as the Germans, the Vietnamese, and the Russians. The answer is pretty straightforward -- these wars were fought far away from American soil. The United States could pick and choose when and where it fought, and in the case of both world wars the US joined the war relatively late (it should be noted that during the Second World War, the United States desired an Anglo-American invasion of France at a sooner date than the British). Moreover, the Vietnam War was a limited war in which the United States put in as many troops as it desired -- until it decided to leave. And, of course, the United States faced an enemy possessing far less firepower than itself.

The American Civil War, on the other hand, was a total war fought on American soil. As others have pointed out, both sides utilized newer (for the time) technologies to devastate the other side, and, in the end, whole cities were burned to the ground in the North's attempt to win the war of attrition against the South (these included mass-produced rifles, distinct from muskets, as well as cutting-edge rifled artillery). But the "deadliness" of the war was not the reason that so many more Americans died than the other three wars you pointed to. It was because these wars were fought in far away lands where the United States could carefully choose when and where it fought.