Certainly, there are a lot of events that rank up there - the Signing of the Declaration of Independence (as well as the creation of it), and probably America's involvment in World War 2. But the Moon Landing was one of the few things that was pretty much an American event from start to finish.
I dunno, fighting for independence against the largest empire at the time and winning with a rag-tag group of militia men was pretty badass. I think it also impacted the future much more heavily than the moon landing.
In fact, I think the moon landing has had the least amount of impact on the world compared to any of the USA's other "badass" moments.
I think landing on the Moon was the most badass event in human history. For hundreds of thousands of years, our species was confined to this little rock, unable to leave a single grain of sand to explore the beach. Held down by gravity, held back by our need for warmth, oxygen, sustenance that can only be aquired on Earth. "No," we said, "this little rock is not big enough for us. We are too badass to be repressed by gravity!"
The only events that compare in badassery are the Lunar Rover missions, when humans went all the way back to the Moon just to drive around on it. Badass.