re: What would the world be like if the NAZIs had won?

The Third Reich had it been successful in its invasion of the Soviet Union, would have been a very difficult enemy to stop. Now, I still do not think that even in this case they would have achieved global domination. It just strains logistics to much to have resources spread that far and thin. Hitler had plans to invade the US, this was one of the last steps in his master plan. However he was wary of the US industrial strength and size. Most likely the Nazis and the US would have entered a cold war for a few years much like the one we had with the Soviet Union. But you said if they WON. So, in that case I would see a war weary Nazi Germany unable to directly attack the US after its successful campaign in Europe and Asia (Russia). Due to this they would certainly have used the alliance with Japan to attack the US from two fronts (much like what happened to them). The result of this would be a defeated America that was territorially divided for the victors. The Empire of Japan would most likely control the western US while the Third Reich controlled the eastern United States. At that point what is interesting to think about is the possible cold war that might take place between Japan and Germany for the ultimate top spot just like it happened between the US and the Soviet Union. So, the short answer is that a mirror history would have unfolded much like today's history but with different super powers and different ideologies.