What are some historically important veto overrides?

Andrew Johnson, an opponent of civil rights, was the president who had the most important vetoes overridden. There have been other presidents with a higher number of vetoes, and a higher number or proportion overridden. But these were almost all about budget disagreements. By contrast, Johnson's veto overrides were almost entirely to do with civil rights and his determination to prevent blacks from getting them.
At the top of the list is Johnson's veto of the first civil rights bill in US history. The bill was aimed at protecting blacks from white supremacist terrorist organizations like the KKK, Redshirts, and White League. For example, the law barred killing someone to prevent them from exercising civil rights like the right to vote. Congress was able to override this veto, and the law was enacted in 1866.
Johnson also vetoed (and was later overridden) admitting non-southern states into the Union that likely would vote Republican. At that time, the Republican party was more supportive of civil rights, while Democrats were considered "the White Man's Party"—as they had been since the days of Andrew Jackson. He also vetoed the admission of former Confederate states in rebellion. Johnson was a proponent of "soft Reconstruction," which meant that states need not approve of the new constitutional amendments protecting blacks' and others' civil rights. Soft reconstruction would have also required a lower number of the state population swearing loyalty to the US.
Johnson's racism, expressed through his vetoes and other actions to maintain white supremacy during Reconstruction, is one of the reasons he is regarded by many today as one of the worst presidents in US history. The damage that he did would take at least a century to repair, starting with the civil rights movement of the 1950s and 60s.