Brown v. Board of Education of Topeka (1954, 1955)

Linda Brown was a third grader in Topeka, Kansas who had to walk a mile through railway yards to get to her segregated elementary school although a white school was only seven blocks away.  The NAACP took her case to test the "separate but equal" doctrine dating from the 1896 Supreme Court decision in Plessy v. Ferguson.  By the time the case reached the Supreme Court, it had been combined with other cases challenging school desegregation in South Carolina, Virginia and Delaware.  In one of the most significant rulings of the 20^th century, the US Supreme Court in 1954 unanimously outlawed as unconstitutional the mandatory racial segregation of public schools that existed in 21 states on the grounds that segregated facilities are "inherently equal."  In 1955, the Supreme Court ruled that schools should comply with the ruling "with all deliberate speed" – which could be (and was) interpreted to mean there was no rush. 

Read the decision: http://www.oyez.org/cases/1950-1959/1952/1952_1/