You've hit exactly upon a Free Response Exam question for AP US History. 1968 was the year I was born, so of course, this was important in US History... all joking aside, the assassinations of Robert Kennedy (who was likely to win the Presidency) and Martin Luther King Jr. (which effectively ended the Civil Rights Movement) were most definitely turning points.
The Tet Offensive in Vietnam also turned a majority of Americans against the war there for the first time since it started. President Johnson then decided not to seek another term, only 9 months before the election. This, among other things, led to the election of Richard Nixon, who definitely changed our history.
Since that was the year I graduated from high school, I remember quite well all of the turning points in American history. In National Politics and the Vietnam War along with the youth revolution in culture, music, feminism, and independence there was a big change in attitude towards the government. When college age students entered an era of rebellion through music, clothes, hair, drugs, etc., student leaders were not hesitant to lead demonstrations against the war. Peace not violence was a big theme that changed attitudes and and the government started to listen. When some of the peaceful demonstrations got violent with the National Guard as in the Ohio 4 killings, parents as well as the general public became involved, so a recall and reexamination of why we were in Vietnam was questioned. Eventually this led to a pull out. As for civil rights, the feminism movement brought about major changes in rights for women, the Equal rights Amendment, employment, and equal pay. 1968 was also the year of two significant human rights leaders, Martin Luther King and Robert Kennedy, and their assassinations. This brought another awareness that things needed to change. I remember this all to well.