At which point would your timeline diverge?

1933 - Hitler becomes Chancellor
1934 - Hitler becomes Fuhrer
1938 - Annexation of Austria
1939 - Invasion of Poland

and cross 1934 out - Hitler was the "Führer" since 1923. 1934 he became chancellor AND reichspräsident in personal union after hindenburg died.

Hmm, I think Germany would have gone on to be something of a powerhouse in Europe, much as it did post-war from the 60's onwards until quite recently.
I know that the Nazis did many terrible things, but before they did those they did much to fix Germany, rebuild its industries and infrastructure, and if peace had been maintained I think Germany would have powered ahead of the rest of Europe...

Hitler had no choice but to go to war. His work creating measures were based on the plan that there would be a war in future. How could you cut the unemployment rate down to nearly zero without employing people in weapon factories or in the construction of roads, and railways and stuff. All of that required a lot of money, and Hitler drove the state into debts. Let's say if there had been no war in 1939, the economic boom would have faded away a few years later and the Reich would have been left on a pile of debts.

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I'm no economist but I don't get the logic behind that. War is an expensive pastime & although on the "winning" side Britain was almost financially crippled in 1945. The country is still paying off the debt now. I understood that Hitler originally wanted to reclaim territories that had been taken from Germany after the end of WWI. I have no idea if he would have stopped there if this had been accomplished without interference from Britain, France or Soviet Russia. I'm quite sure he never thought it would become the long bitter war that it turned out to be.

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Bismarcks unification in the 1860's was also based around the concept of war (Blood and Iron, Railways and Rifles etc). Defeat those that are opposed to you and you're free to do as you will. And as Trotsky said, War is the locomotive of history.

Hitler wanted to "right" the wrongs done to Germany in the wake of the First World War. He also wanted to wipe out communism. The latter was always going to involve invading Russia and therefore he had always planned for war.

And if WWII hadn't happened. The USA might still have it's head in the sand as far as world affairs go.

Hitler was in prison until December 1924, hardly in a position to influence power despite his little band of followers.

WW2 pulled Germany as well as the US out of the Great Depression.  Germany's answer was called "National Socialism", "socialism" not being a dirty word at the time, but being extermely nationalist and hardly socialist.  The US answer was "Roosevltian socialism" (my own term for the New Deal and carrying every connotation of the dirty word).

Did European socialism influence American socialism or was it inevtable?  I believe that American socialism was inevitable.

I can not see a continuation of Hitler's power without war.  He surely would have been deposed by one means or another by, let's say, 1945.  Can we assume his racial policies would have remained in effect until his death?

Depending on the "brain drain" of Jewish and other minority scientists under Hitler's theoretical peaceful rule:

Germany would have been the first country to develop practical peaceful nuclear fission.

Germany could have eclipsed the US and the Soviet Union in the space race (the majority of early space technology scientists being captured German scientists).

Germany's technlogical advances would have ensured its financial future well into the 1960's, until it had to compete with Japan.

Militarily, a united Germany may have contributed to a faster end to the Cold War, or it could have incited a nuclear US/Europe v. Soviet Union nuclear war.  But since that's not the original question I will refrain.

War creates new technlogies but stifles others.  Televison was well on its way before the war.  Radar and predecessors of GPS were the result of war.  Who can say what would have happened if transistor and miscoprocessor research had continued unabated during the war years.