In foreign policy, the main event of 1968 was the Tet Offensive. This offensive, launched by the North Vietnamese at a time when the American government had been saying the war was almost won, showed that the government had been misleading the people. It also convinced many people that the war could not be won. This is seen as the beginning of the end of US involvement in Vietnam.
On the domestic scene, 1968 was a year that helped bring about the polarized politics we now have. This was a year in which Richard Nixon ran on his "southern strategy" against the Democrats. It brought in an era in which politics would become split along racial lines and also along the lines that have since hardened into our "culture wars." This was the split between Nixon's "silent majority" of traditionalists and the liberals who believed that society should change. This split was brought about, in part, by disgust on both sides at the events of the Democratic National Convention in Chicago and by the assassination of Martin Luther King, Jr. and the riots that followed it.
In these ways, 1968 led to US withdrawal from Vietnam and the lasting shadow of the Vietnam War on American attitudes towards engagement in foreign countries. It also helped lead to the polarized culture wars that still exist between traditionalists and liberals.