Depends on what we are discussing. In terms of defending the country, it is the United States Navy- unless you want to discuss some bullcrud/MW2 way of infiltrating the country, you have to go through the USN. The Air Force and Army are also extremely important in this regard, with the National Guard still in front of the Marines in defense.
If we are discussing an operation that brings our military abroad, you must then ask yourself what sort of operation it is. The Navy is vital in all areas and the Air Force is critical. The Marines and the Army are both suited to do whatever needs to be done- contrary to popular belief, while the Marines do train longer than your average Army grunt, they aren't this elite shock force that compliments the Army. I would also take Rangers over the Marines.
No one single force is more important than the other. However, the Marines are the least useful in defense and the National Guard, while it bolsters the numbers of the Army in the current operations, is the least capable of all the branches. The Army is extremely important as is the Air Force, but the USN is the steel backbone that projects America's military strength abroad while also assuring the defense of the homeland. It is the siren song of other nation's governments if they oppose us- Clinton once said that whenever a Crisis broke out, the first thing asked was, "Where is the nearest carrier?"
The USN is the dagger, sword, shield, bow and arrow, cannon, and armor of the United States.
@ Fox:
The United States has deployed a large magnitude more troops than any other nation has in the ongoing operation in all branches. That makes the likelihood of screwups and mistakes far, far, far higher. If the numbers were reversed, I would say that it is likely you would hear of many British military foul ups. It also doesn't help that this large, massive force is fighting a war it is not trained for- and is more often than not just sitting around.
Remember, it is all about numbers. The United States invaded with 248,000 soldiers and the UK used 48,000- the UK's occupation force was around 10,000 and the United States' hovered anywhere from 85,000 to over 150,000.