Not unique and not uh, not shared with general Western Europe. UK for example: Saxon, Viking, Celtic, Roman, just about every other European ethnicity has been involved in its making and population (not to mention the contact with "Saracens" during the Crusades and the huge influence it had on philosophy, architecture and other aspects of the culture) and in more recent, modern times, massive influxes of Asians, Caribbeans and Africans, too, which is ongoing. Most British cities (and French too) have whole regions where you can barely find a shop front or passer by that can tell you anything in English. There are those who say that's a bad thing, though I love, embrace and welcome it.
Ooh. So that's not even unique. Interesting.
Looking from the outside here, I'd say what stands out to me as being different to Europe is the intensity and ubiquity of the patriotism you got going on over there, first off.
It can be pretty creepy at times. Do you know that I've been called Un-American by some people just because I was caught drinking a tea other than ice tea? And let's not forget the people who complain about having to buy anything not made in the US (not just Chinese, I mean any other country) because they believe it must be of inferior quality if it wasn't made by Americans.
There are also people who will really make a scene if you suggest that capitalism and our form of democracy are anything less than perfect, even under circumstances where their shortcomings are glaringly apparent (which is ironic, considering that one of our ideals is supposed to be the freedom to question things).
Also, a general ignorance and disinterest in the wherabouts even, let alone the languages and cultures of the non-English speaking world.
Oh my. That's actually a cultural trait? I had dismissed it as an example of backwardness and uneducated behavior that needed to be improved.
It does explain why I'm constantly having to explain to people around me that capitalism wasn't "invented" in America, that several of our ideals were influenced by Enlightenment thought, certain elements of 18th century British culture, as well as ancient Greek and Roman ideas. Often they continue to insist that certain things are uniquely American when they aren't.
The worst is when they accuse me of being unpatriotic for pointing out such facts.

Now I just keep my mouth shut (except on here), I don't want to anger those people.
And unashamed capitalism - sure it's as rampant as anything else in the UK and perhaps Germany (less so in those countries that have Mediterranean coastline, in my observation), but there's a sense of "filthiness" and guilt about it still that I don't see in American culture, where it's praised and encouraged.
Not only that, you can actually be ridiculed for doing anything other than praising capitalism. One of the biggest problems with it that I've experienced first hand, is that it can be very, very difficult for someone to hone their skills initially if people are primarily looking for those that have already proven themselves. It works well when the labor pool is smaller, but can be grossly unfair when it's larger. It's also very hard on skilled people who don't tend to be competitive or pushy by nature.
And the idea of never having to get out of your car or actually be outdoors in the open air if you can help it ... heheh... at least that's the impression I get when I visit my sisters in NC!
Oh my, don't get me started on that one. I don't have a driver's license, and it's very hard to get around without a car. To some extent I'm even looked down on for being afraid to drive. I really don't get what's so great about driving a car, though. It seems wasteful and unnecessary, especially to design cities around having the things.
I've heard that in cities like New York, though, they rely more on public transportation. So it's not like that everywhere, thankfully.
I'm sorry that I can only think of things that are bad to my mind, off the cuff... I'll come back later if I can think of more positive things... though one positive thing that always leaps to my mind about American culture is Mark Twain - and rock n roll, of course!
Oh, don't feel bad, I have trouble thinking of good things myself at times.

Thanks for helping me note some things I normally dismissed as annoyances rather than seeing them as part of our culture.
Ultimately, what I do like about America, is that we have more wealth, and more job and education opportunities overall than many other countries. We also have a lot of volunteers and social programs to help the less fortunate. That's what really keeps me from disliking us... I mean, at least we've got opportunity and compassion. That makes up for everything else, I suppose.
there's an old joke been floating around the UK for decades: what's the difference between a pot of yoghurt and the USA? - If you leave a pot of yoghurt out for 400 years, it'll develop a culture
So, it sounds like you people have noticed the lack of distinctive culture as well? I guess that means there might be something to it.