The trials, in southern Germany, involved senior members of Adolf Hitler's administration being brought to justice by the Allies.
All of the twenty one defendants who went on trial in November 1945 pleaded "not guilty" but the evidence was overwhelming.
One of the American prosecutors who helped to convict top Nazi officials, Whitney Harris, said that at the start of the process they had no inkling of the extent of the atrocities they committed.
"I did not have the slightest idea of the scale of the genocide that had taken place in Germany. We did not have much solid evidence when we started," he told Der Spiegel weekly.
The picture of some of the worst crimes ever committed emerged, as Nazi officers revealed under questioning how SS commander Heinrich Himmler had ordered Auschwitz to be turned into a mass extermination camp for Jews, Gypsies and prisoners of war.
Of the 1.3 million people sent to Auschwitz, 1.1 million died.
Sentences
By October 1, 1946, eleven had been sentenced to death and seven had been handed prison terms. Among them was Hitler's deputy Rudolf Hess who was condemned to life imprisonment.
High drama erupted when Hermann Goering, one of the chief architects of the "Final Solution" to eradicate the Jews, committed suicide by taking cyanide in his cell on October 15, 1946, on the day of his execution.
At the anniversary ceremony, some of the last surviving witnesses from the trial have been recounting their memories. Reporter, Susana von Paczensky, said the defendants looked dishevelled.
“Goering, everybody had been afraid of him, but also had admired him. And he looked like an old woman, like you should cheer him up and give him something warm to drink. They all looked like they could be sitting on a street corner and beg,” she said.
The 10 others were hanged.
Three defendants were acquitted.
Martin Bormann, was condemned to death in absentia, though it later emerged that he had died in 1945.
Nazi dictator Adolf Hitler never faced trial, having killed himself in the final days of World War Two.
What shocked many at the trial was the refusal of the defendants to accept personal responsibility for their role in the crimes carried out by the Nazi regime, maintaining that they were merely obeying orders.
"I did not expect them to be such pitiful cowards," Arno Hamburger, a leader of the Jewish community in Nuremberg who acted as a translator at the trials, told the Sueddeutsche Zeitung.
The birth of International Criminal Justice
The proceedings are widely seen as laying the foundations for subsequent international war crimes prosecutions.
The International Criminal Court (ICC) president Philippe Kirsch, said the trials that began here gave birth to the concept of international criminal justice.
"Even ten years ago, I still regarded the Nuremberg process as no more than an historic event, but now I have come to recognise that this was where the idea of international criminal jurisdiction began," he said.
The mayor of Nuremberg Ulrich Maly said the city had wanted to show the enduring legacy of the trials which made the world aware of the horrific crimes committed by the leaders of Nazi Germany.
"We should not lose sight of the role of the United States in the Nuremberg Trials. But we want to emphasize the significance of the Nuremberg Trials for a global form of justice and draw the link to today," he said.
Former Nazi prosecutor Mr Harris said he believed that the main message of Nuremberg was one against war.
"We cannot tolerate wars in this world anymore. Adolf Hitler was only a name that symbolised the absolute and worldwide breakdown of morality in the 20th century. All these gruesome crimes are not exclusively a German phenomenon."