This is a topic that is probably positively quaint to anyone born after 1980 or so, but seems to be burned rather deeply in the consciousness of Americans my age and (especially) older. Many are amazed when I tell them that I only heard one reference made to the "c-word" my entire time in Vietnam, and even then it was pretty benign.
I have to say that I didn't give the "c-word" much thought myself until my passport arrived back in the mail from the Vietnamese embassy, with a page-sized visa pasted in, at the top emblazoned "The Socialist Republic of Vietnam".
The "c-word" in question, as I'm sure you've guessed by now, is "communism".
Vietnam is nominally a communist country. Actually, it's a Communist country, which means that you can belong to any political party you like as long as it's the Communist Party. To be sure, political dissent is not officially tolerated in Vietnam, and one way I could ensure myself a rapid expulsion from the country would have been to actively promote democratic reform (the other would have been proselytizing). Not a problem, as I am interested in neither.
The reality is that "Communist" in Vietnam today does not--at least as far as I could observe--have anything in particular to do with actual communism. (Sort of like "Republican" in the US today has nothing to do with actual republicanism.) Market-based reforms (Đổi Mới, "renovation") have been underway since the mid-1980's, and business has been booming ever since.
In fact, I would say that the typical small business owner in Vietnam has a damn sight more freedom (or at least, non-interference from the state) than their American counterparts. Just try setting up your Sterno burner, grill, and cooler full of meat and condiments on a sidewalk in an American city, selling food to passersby, and see how long you're there before you're shut down. Just try renting bicycles or motorcycles out to tourists without filling out any paperwork.
To be sure, there might be a lot going on behind the scenes there that I just didn't see. But it's pretty jarring to walk into restaurant now and see the profusion of officially sanctioning documents (food service license, liquor license, health inspection, etc.) so prominently displayed.
Beyond communism as economic system, there was really very little of the cultural trappings of what I associate (perhaps erroneously, perhaps not) with a single-party state. Ho Chi Minh's image is fairly ubiquitous (especially on the money; he's on every denomination) but not noticeably more so than, say, George Washington's is here (particularly in the city that bears his name.) If there were any big portraits of Vietnam's current political leaders, I didn't see them. In fact, I would have to look up the name of the current head of government, and I just spent three weeks there.
I didn't see any gratuitous displays of military might. In fact, I didn't see that many cops--certainly less per capita than in say, Durham. There are a lot of people in uniform, but if you look closely, many of them work for private security firms.
But perhaps the best example I can think of is this: there are stores that sell old propaganda posters. They have signs hanging over them advertising "Old Propaganda Posters!"