The common term was "flower power" and it wasn't the name of a movement, it was just a common phrase uttered by those protesting the Vietnam War in the late 60s. It was part of the Anti-War Movement, for which literally every American was forced to choose sides. There wasn't much call for the legalization of drugs, many of which were already legal when the decade began, and only were legislated to be illegal as adventurous people discovered them. The primary demands were an end to the war and an end to the draft. Many thought that an end to the war could be brought about sooner by adopting an attitude and philosophy of peace and love, and flowers were a featured player in that philosophy, so the catchy term Flower Power started appearing on protest signs of the time.

By the end of the 60s, protests were becoming increasingly violent as desperation towards the war and the draft increased. Protesters were shot and killed at Kent State and other campuses in 1970, campus buildings were occupied by protesters and even bombed. Peace and Love had failed, and nobody was calling for Flower Power.

Another common demand was for allowing 18 year olds to vote. They could be drafted and sent off to war to be and be killed, so it seemed fair that they should have a say in the issue, and in 1971 they were granted the right to vote. In 1973, the draft was abolished.

Another outgrowth of the movement was the Environmental Movement, which led to the founding of the Environmental Protection Agency and the anti-pollution legislation.