America is a country born in revolution and come of age in civil war.
Basically, it was a country that was "settled" by people who liked to fight, and who were "troublemakers" in their home country. Which is why an embryonic nation could wage a war against its mother country and win. This was true not only of the original settlers, but of most of the people that followed. Their heirs inherited their genes, and probably a number of "traditions" that sprung from that way of thinking.
There is a great gap between rich and poor in the United States. Poor people (African-Americans in inner cities, poor whites in the countryside) live in areas where there is a lot of "gang-fighting" or "brawling." For such people to serve in the military is for them to get (relatively) good pay to live a life like the one they are used to.
Many of these poor Americans are willing to "go for broke" to get rich. This do-or-die mentality was the motto of the 448th (Japanese-American) Regimental Combat Team of Senator Daniel K. Inouye. The military (and the wild west) is in a sense, an expression of the American way of life.
As for risks, probably Patrick Henry spoke (in 1775) for many (later) Americans when he shouted: "Give me liberty or give me death."
There was a Roman saying, "dulcet et decorum est pro patria morir." (It is a sweet and beautiful thing to die for one's country.) On the surface, it seems like a form of patriotism, but is real meaning may be, "the Roman standard of living so much higher than every one else's that I'd rather be a dead Roman than say, a live (and probably enslaved) Carthaginian." As members of the richest and most powerful country in the world, Americans often feel that way.
As for Australians (to answer questions in the comments), the ethos is quite similar. The continent was initially settled by "convicts," people who liked to wield arms almost by definition. This ethos is exemplified in the following Australian song: http://en.wikipedia.org/wiki/The_Wild_Colonial_Boy
It's about a robber who would rather fight at the odds of one to three than to surrender (and be hanged). He gets to shoot one of the cops in exchange for his own life. Modern Australians (like modern Americans) are the descendants of such people (the survivors, that is).