Wernher von Braun was a Nazi rocket scientist that helped design the V2 rocket. After being captured by the Americans, he became the foremost engineer for NASA, and led the team that created the Saturn V rocket - the one used on the first moon landings.

Werner Heisenberg, the discoverer of the famous Heisenberg uncertainty principle, made many of his contributions to the field of particle physics while working in the Nazi nuclear program.

The concentration camp medical experiments also made considerable advances in organ transplanting.

You may find this article interesting, as it deals with the ethics of using Nazi medical data, containing information about various trials done at concentration camps etc.

The article's provenance is a Jewish Law website, so it may have some bias, but it seems to be well sourced.

Much of our knowledge of hypothermia comes from the Nazi experiments in Dachau. They submerged prisoners in tubs of ice water and then studied different methods of rewarming them. Although most of the information was destroyed, much of it was recovered. You can read all about the experiments here: http://www.nejm.org/doi/full/10.1056/NEJM199005173222006

I have heard that without their radical methods we would not know some of the things we do today without them

I am assuming that by "radical methods" you mean human experimentation so I am going to concentrate on that.

This trope is very commonly trotted out, but it is really without merit. There are several reasons why the results of Nazi doctors' human experiments are not useful:

• flawed premises: a prime example is the most infamous human experimenter, Mengele in Auschwitz. Most of his experiments relied on theories about race that have no scientific basis. His major aim was to establish genetic differences between Jewish versus Germanic or Aryan reactions to disease and other physical characteristics. The genetic angle is why he used twins, by the way. His reasoning was that if the twin pairs consistently showed different reactions the issue couldn't be genetic.

• flawed methodology: the physical condition of the human test subjects was too aberrant from the norm to allow for scientifically acceptable conclusions to be drawn. They were weakened by hunger, disease and overwork and thus any reactions they had to certain stimuli do not reflect those of the average population. Other methodological errors include: no double-blind trials, sloppy record-keeping.

• falsifying of data: there was no scientific oversight on the experiments and every reason for the doctors involved to manipulate the data to fit what they or their superiors wanted the findings to be, either for reasons of self-promotion or to toe the party line or in apprehension of a backlash if the results were deemed unacceptable. A totalitarian environment is not generally conducive to free and untrammeled research.

In addition, many records have been destroyed as the German defeat became obvious and the doctors were aware that their "experiments" might not reflect favourably on them. So there is really not much left of the "research" anyway.

Those are just a few things to keep in mind when doing your research and writing your paper. I am not going to do all your work for you and give you a laundry list of sources, though.

Not much. Datasets were gained on certain things, such as hypothermia and exposure to high altitudes.
See this, which was already posted. The data is useable, but not very good. You may wanna check out this layman's article about it.

And that's the better material from human experimentation. Many experiments didn't produce useable data at all, and others couldn't've even if the experimenters had done them properly because there was no actual experimental procedure--it was just scientists torturing people. See my previous answer here.

Note I'm talking about the human experimentation bit of their science. Other scientists working with the Nazis did have more success in areas other than human experimentation (though many still had ethical issues, such as von Braun using slave labor).