Nazi symbols were ubiquitous in public space in Nazi Germany: Hitler portraits in public buildings, swastikas, memorial statues to events considered remarkable by the Nazis like the 1923 Putsch. There are still some statues around which were set up during the Nazi period (mainly naked men and women with tight butts), but I have never heard of a Hitler statue anywhere. I heard about Hitler busts which were displayed in public buildings, but I have never heard of a statue in a public square.
On the other hand, Stalin had statues built of himself during his lifetime, as well as Salazar apparently and Franco, as well as Mussolini. Were there actually Hitler statues I am not aware of? Were statues planned but never built? Or were statues of Hitler not in-line with Nazi aesthetics/ideology of art?
Edit: My intention is not to equate Hitler with the other people I named. I simply wanted to point out that powerful people building statues of themselves was not uncommon during that time.
2nd edit: I have received messges of people telling me there were indeed Hitler statues, presenting me life-sized busts of his head as evidence, which were displayed indoors. Please not that I am not talking indoor busts but full statues. I feel that busts follow a different art-historical tradition and invoke different associations in propaganda than full body statues in public squares, which is why I would like to seperate busts from (complete) statues. However, if someone can convincingly argue from an art-historical perspective that indoor busts follow the same tradition as outdoor statues and have an interchangeable purpose in propaganda (which I find hard to imagine!), I would by satisfied.
The lack of statues of Hitler mainly depends on two factors:
A limited timeframe / tradition
In 19th and 20th century Germany, as in most of Europe, statues were mostly reserved for royalty, generals and statesmen. While Kings and Emperors got their statues more or less automatically, generals and statesmen had to prove themselves in order to receive such an honour. Given that this usually, especially for politicians, takes up quite some time; it becomes clear that the window for Hitler to achieve the status required/expected for a statue was very much limited.
Hitler gained dictatorial power in 1933, but had done little to merit the placing of statues in town squares:
It wouldn't be until 1938 that Hitler accomplished something that could be undeniably marked as a truly momentous feat with the annexation of Austria into the German Reich.
Still, would this have warranted a statue? By comparison, the first public statue of Otto von Bismarck dates from 1877. It's difficult to compare events like these, but I do not think that anyone would seriously argue that the defeat of Austria-Hungary, France and unification of Germany as a nation state did not outweigh the Anschluss in political significance; yet Bismarcks first statue was placed some 6 years after these events in which he played a pivotal role. Still more telling: the vast majority of Bismarcks statues were created after his death in 1898, which - in any case - is much more common than statues being erected while the subject is still alive (and their legacy still open to changes).
Given the time it took for Bismarcks first statue to be erected, it's unsurprising there were no statues of Hitler placed in town squares during the brief period between march 1938 and september 1939. Which is not to say that many towns did not do other things to publicly praise Hitler; in fact hundreds of towns renamed their (main)square Adolf Hitlerplatz in his honour.
After the Invasion of Poland and with Germany in a still undecided war however, it would have been a sign of grave hubris to place Hitler statues in any square or park. This is not mentioning the fact that the materials for such a monument would have been needed for the war industry anyway.
Personality cult / Nazi ideology
Now one might say that the limited timeframe was insignificant, because Hitler was a dictator who could have demanded statues of himself raised in every village in Germany if he wanted to. The thing is that he did not seem to desire this and this is fully in line with the nature of Hitlers cult of personality and the ideas of national socialism.
Hitlers personality cult was carefully crafted to portray Hitler as Germany's savior. The image it (and he) presented was one of self sacrifice, rather than ambition. A man who had set his personal life, wishes and desires aside to restore Germany and the German people to greatness. In effect it meant that Hitler was a man with a mission and that praise in the form of statues and monuments would only be appropriate when this mission was fulfilled.
This was in full accordance with the broader the national socialist ideology which put the people far above any individual. National socialist architecture and art echoed this, for example:
Most of the Hitler-paraphernalia were not produced by the state or government. Most paintings, photographs, statuettes and (gypsum) busts were made by private companies . A (fairly limited) series of postal stamps with Hitlers portrait are just about all that the German government produced with Hitlers likeness on it. Similarly, most of the Nazi propaganda posters do not portray Hitler; but instead feature idealized versions of German children, soldiers, workers or mothers.
So in summary: the fact that there were no statues of Hitler placed in public spaces was due to:
If you're interested, I'd especially advise reading The "Hitler Myth": Image and Reality in the Third Reich by Ian Kershaw. It's still the best book out there when it comes to how and to what aim Hitler and the Nazis sought to portray themselves to the German public.