I can speak to Germany - the most brutal and insane of the three Axis powers.

It's important to note first off that many of the horrors we associate with Nazism - the eastern front, Auschwitz, forced labor, eugenics - would not have been immediately apparent to the average German in 1933. The average German was not voting for war with Russia, they were voting for a millennium, for a national renewal. If he had promised a 6 year war that would kill millions of Germans and a death camp that would kill all the Jews in Europe, it is very unlikely he would have been elected. They elected him for an [often incoherent] message that promised a return to greatness, and a return to the simplicity and prosperity of a past time, and the dismantling of the widely despised republic.

So why did Germans continue supporting the regime when the insanity and brutality came into full effect? Hitler was very clever about dialing up the insane aspects of his regime. When shortages and hardship threatened, Hitler would seek out diplomatic or military victories. Though the average German very likely did not want a war on the scale of World War One, they caught war fever with victory over France in 1941. This victory would have made Hitler seem like an absolute god to many Germans. It was one of the most complete humiliations of a foreign power ever inflicted by another foreign power, and the only major power the German army defeated and occupied outright. It was an undoing of all of the humiliation of Versailles; there was much more buy-in to war after this point. Hitler was able to keep delivering victories for years. He was also willing to loot the resources, especially food, of occupied nations to ensure the German people didn't starve as they had in World War One.

Whatever excuses they made after the war the military would continue giving their all important support until defeat loomed. I talk a bit about the military's reasons for supporting Hitler in this post.. The 1944 movement sometimes obscures the fact that military was a pillar of the Hitler regime, just as it had been a pillar of the Kaiser's.

With the support of the military and a large police force it should finally be noted that many in fact did not support the regime. The role of coercion and fear by the security apparatus played a major part as well.

Of course, this could go much deeper. Let me know any follow up questions you may have.