As someone who has visited Auschwitz and had relatives die in the holocaust I understand the atrocities committed by the Nazis and don't mean to make light of these acts or make them seem any less cruel than they really are. But I've always been curious, did any of the medical experiments done by the Nazis and Dr. Mengele provide any advances or breakthroughs? Also did the Nazis make any scientific breakthroughs?
The first person to come to mind is Wernher von Braun. In a nutshell, von Braun was at the forefront of the development of the V2 rocket for the Nazis. Von Braun defected to the United States in 1945 and immediately went to work for the US Army in developing ballistic rockets for the Americans.
This work in rocketry lead directly to his work in developing the Saturn V rocket, which was most notably used in the Apollo space program that led the Americans to the moon (from Apollo missions 4 to 17).
While the Nazis engaged in unthinkable atrocities, their scientists have contributed greatly to the body of science we still use today. Both the fields NASA rocketry and jet propulsion (specifically at the Jet Propulsion Laboratory) benefited directly from Nazi scientists.
Biography of Wernher von Braun: https://history.msfc.nasa.gov/vonbraun/bio.html
Overview of JPL history: http://www.jpl.nasa.gov/about/history.php