For me, personally, I am Indian (native) and then I am American. The American dream was not a reality for indigenous peoples here until 1924 when we were granted citizenship to a "country" that was our own. Yet, even with this new right, we still were not "citizens" until the Civil Rights era - but enough of that...
When people fabricate and belittle the culture of "America,"I become compeolled to say that we have a vibrant, rich culture. Native peoples have celebrated their culture, their sacred dances, ceremonies, sacred lands, etc. for 15,000 plus years here (part of America!). Artifacts and history proves this. By virtue of this country being where it is, regardless of the political, religious or any other propoganda others might try to impose, America flourishes in many regards as it relates to culture (historical perspective).
There are many things I could add here but many have already been said; as for others - sometimes it is just best NOT to post a reply...
To echo YAG, and better answer the OP, what makes me uniquely American:
I'm part Cherokee on my mother's side. On my father's side, I have ancestors who came here on the Mayflower. Also on my father's side, I have ancestors who immigrated here as poor German farmers. My family's history embodies several different facets of American history. The cultures of all the people who migrated here and gave birth to a new culture, and eventually to me, is part of my American identity. I have roots in England, Germany, France, Italy, Ireland, and the Cherokee people, as far back as we can trace them.
As for our American culture... well... I listen to jazz and hip-hop and rock and roll, I enjoy products manufactured on assembly lines, I use the internet, I watch American movies and American television, I speak and type in English online because this the most commonly language used in the US, I wear American tennis shoes and American brand clothing, I eat American fast food and drink American cola, I enjoy chocolate, tomatoes, corn... of course, so does everyone else in the world. All those people that have convinced themselves we have no culture, so I'm not sure where they think they've been stealing those things from. So... none of that makes me especially unique in the world. I also enjoy many things from other cultures and countries. That's alright though, I've long considered myself more a citizen of the world than any one nation anyway. I love this area, too, because more than any place else in the country, even New York or LA, you can see the melting pot in effect here. Go to Tyson's Corner mall for instance and ask at random the first 20 people that walk by which country their family is from and you'll probably get 20 different answers. You'll probably even get 4 or 5 different continents. Yet, if they don't consider themselves Americans now... then their children's children certainly will. and they'll all add something new to the mix.
I do drive a muscle car... I guess that's pretty distinctly American.