1968
Of course this year had its share of pop culture events and icons but each year has many of those.Here's why 1968 might be the most important year in the history of the United States of America:
The civil right's movement, after the death of MLK, sees more successes, albeit tragic that it came in the wake of who proved to be quite a wise civil leader. Very rarely do you find someone that practices non-violence when violence could be the answer, of course there are other examples, like Gandhi, but again, it is rare and should be admired.
On top of that, the Democratic party was on the brink of destruction, the death of RFK caused massive party splits, and the primary hosted riots and violence, as well as the eventual candidate, who would go on to lose to...
Richard Nixon, who ushered in the era of the modern Republican party. Why is this important? Before 1968, the South voted blue, afterwards, it would become the strongest Republican region of the US. This political tango undid what had been essentially set in stone since the end of the Civil War, and the parties had flipped policies and geographical bases in what turned out to be a low for the Democratic party. (Although, it must be noted, an independent candidate carried 5 of the southern states, a remarkably good run for candidate not running under one of the two major parties)
Add on top of this, the increased manpower and strain of the Vietnam war as it reached its height during the Tet Offensive, which put America on its heals as the Viet Cong lashed out all across the country, in what turned out to be its last sustained campaign of the war (North Vietnamese forces would have to do the bulk of the fighting, as many, many Viet Cong died in the first few months of 1968). This, of course, led to stagflation and the economic problems of the late 60s/early 70s. Also worth noting, is that the People's Republic of China (The Communist-led government of mainland China) and the USSR (The Soviet Union) had a brief border war, further dividing the two, allowing the U.S. to gain influence in China in the next few years, the first time since 1949, after the Communists forced the Nationalists off of mainland soil.
I'm sure I've forgotten a lot, but this is definitely one of the most important years in the cold war (China/USSR & Vietnam) and U.S. Politics (Assassinations, civil rights movement, a huge switch in voting blocs). While maybe not top 5 in world history, this might be at the tail end of the top 10, as I can only really think of 2-3 other years in which more changed in a short amount of time in the 20th century.