Firstly, segregation has not quite ended in the United States. There is a difference between de jure segregation, which sanctified segregation by law, and de facto segregation, in which the system exists through racist habits or policies that are indirectly racist. One such example of indirectly racist policy is a form of gerrymandering that excludes certain neighborhoods from a school district due to a higher concentration of minorities or the potential for a higher concentration of minorities due to lower property taxes.
In regard to your question, however, I would say that Brown v. the Board of Education of Topeka, Kansas, in 1954 was the first significant case to end segregation in a key space of public accommodation—schools. This was followed by Brown v. Board II, which was decided in 1955. This ruling demanded that Southern states proceed with integration with "all deliberate speed." This was meant to ensure that the ruling would actually be carried out. However, the first school to be integrated, Little Rock High School, was not integrated until September 1957.
The third case, which dealt more directly with the impact of Jim Crow in people's private lives, is Loving v. Virginia, which was handed down in 1967. The Lovings, who are quite appropriately named, were an interracial Virginia couple. Richard Loving was a white man married to a black woman. Their relationship caused them to have to hide to avoid arrest, though they were sometimes unsuccessful. The Loving case struck down laws that forbade interracial marriage. Such laws did not only impact black and white couples. On the Pacific coast, particularly in California, there were also laws that forbade intermarriage between Asians and whites.