Was Volkswagen actually the brainchild of Adolf Hitler, or is that a modern myth?

That's actually true. He wanted a car produced that had 4 seats, could hold a traveling speed of 100 km/h, was economical in its fuel needs and should cost no more than 1000 Reichsmark. Since the existing car companies did not think that this could be done, he tasked Ferdinand Porsche to design such a car and the Deutsche Arbeiterfront (German Workers Front) to build a factory to produce the car.

The result was the KdF-Wagen (KdF="Kraft durch Freude"="Power through joy"), a predecessor of the Volkswagen Beetle.
Fun fact: Wolfsburg, the city the Volkswagen company has its headquarters in, did not exist at that time. It developed around the new car factory and was first called "Stadt des Kdf-Wagens nahe Fallersleben" (City of the KdF-Wagen near Fallersleben).
There were plans to rename the city to Adolf-Hitler-Stadt (Adolf Hitler City), but this did not take place due to WW II. After the war the city was renamed to the name of a medieval castle nearby, called Wolfsburg (Wolf's Stronghold).