During World War 2, what government branches, if any, existed in Germany? I've always heard about the Third Reich and Hitler, but I never heard about the rest of the government.
The government of the Third Reich evolved and subverted the institutions of the parliamentary Weimar Republic established in 1919.
Before the ascension of the Nazi party in January 1933 the legislative branch of the government was comprised of the Reichsrat, representing the various Länder (German states) and the Reichstag, a parliament elected according to a system of proportional representation.
As soon as Hitler gained power he began undermining the power of these branches of government and working towards a centralist, totalitarian dictatorship. These changes occurred incrementally:
So by 1938 local and state governments were controlled by Nazi Party leaders, known as Gauleiters. The central government itself was made up of competing, overlapping power structures all vying for personal power. The result was a convoluted and often divided administration with a tendency to implement the more radical and extreme elements of Hitler's ideology in order to gain favour with Hitler.
There are two opposing opinions on the efficacy of this system (from Hitler's perspective). 'Intentionalists' believe Hitler created that system to ensure the total loyalty and deduction of his supporters and prevent conspiracy and betrayal. 'Structuralists' believe that the system evolved by itself and limited Hitler's totalitarian power.
Source: Nazi Germany: Administration on Wikipedia