In the Mass Effect fanfic series Uplifted Hanala seems to enjoy stealing Hoch's cap. Rundstedt forces SS officer Joachim Hoch to give his hat to his granddaughter as a form of humiliation, telling him that he is not a real officer. Rommel seems to have a tendency to fiddle with his.
M.Bison (played by Raul Julia) wears one in Street Fighter. To further stress the Putting on the Reich aspect, the metal Shadaloo symbol on the front looks rather eerily like a mix between the Nazi "Reichsadler" and the SS "Totenkopf" motif.
One is part of the regalia of Paradorian President-For-Life Alphonse Simms in Moon Over Parador. Richard Dreyfuss wears it with a jaunty tilt that makes it much less impressive.
Frantic. Michelle wears one when she first meets the protagonist played by Harrison Ford, along with a black leather jacket.
Seems to be part of the Star Fleet dress uniform in Star Trek Into Darkness. Particularly visible in the gathering at the end of the film.
In Dan Abnett's Gaunt's Ghosts novel His Last Command, when Ludd is sent to get troops to the battlefield, he loses his cap getting there — across the battlefield — and their first question for him when he said he was a commissar was to ask where his hat was. (He gets them to the battlefield anyway.)
In Honor Harrington, the Grayson Space Navy's uniforms seem to be modeled after the US Air Force, so naturally they have these, complete with gold oak leaves and lightning bolts. It's stated that they seem to weigh at least 3 kilograms and cause the title character to feel like "some comic-opera costumer's idea of a prespace military dictator".
Naturally, some of the Soviet Officers in the RedAlert games wears these.
M. Bison from Street Fighter is never seen without his hat, except in one DLC costume. To further stress the Putting on the Reich aspect, the metal Shadaloo symbol on the front looks rather earily like a mix between the Nazi "Reichsadler" and the SS "Totenkopf" motif. And now Cammy has one, as of her second DLC costume.
Major Rezner of the Eisengrad Army wears one in MS Saga: A New Dawn, along with a few other officers. It's always fun to have her finish off enemies with a Beam Pistol shot.
Comrade Black, Big Bad of the de Blob games, has one that's as tall as he is. As do all his statues and his personal mech. He is careful not to lose it, even when he's been stripped of his resources, his military, and finally his clothes.
Dawn of War: the commissar's portrait is half hat, half Judge Dredd-esque chin. When Commissar Anton Gebbet is killed by the invading orks in Dark Crusade, Warboss Gorgutz notes that he liked the hat, too bad it was lost along with his head.
Rocky the Flying Squirrel would occasionally wear one while announcing a commercial break.
It was certainly a must for Fearless Leader.
The "Banana Republic" in DuckTales and Thembria in TaleSpin have people wearing these hats. Baloo wears one as well, albeit a less decorated one.
Played straight in Real Life in the 1990s with Russians with Rusting Rockets and Russian cops. Unlike Reds with Rockets, they have these as part of uniform. But the caps are going to be abolished soon, replaced with smaller ones in the older Soviet style. Soviet officers did often have this kinds of caps as part of the dress uniform (hence the trope name), though Soviet caps were not quite as large as modern ones.
An overview of Soviet uniform caps may be found here, showing civilian and military caps from various decades, with different designs—the collector's photos are widely copied for other websites.
Modern huge peaked caps are disliked among the Russian military, derisively known as "Pinochet caps". They are also a case of Sukhomlinov Effect, becoming larger and more fanciful as the Russian army weakened and grew underequipped and undertrained.
As of recent years, Russian military funding has risen again, and coincidentally, they have adopted smaller caps lacking the double-headed eagle of the Russian federation and look similar to Soviet caps.
Across the world, this is a common feature of the uniform of high-ranking officers in the military and many civilian law-enforcement agencies in many Western nations have something like this as part of the uniform (or at least the dress uniform). In most of these cases, however, they tend to be smaller and a bit more modest than the stereotypical authoritarian model.
On the other hand, for much of the Cold War, large-crowned American caps were bigger than their Soviet counterparts.
The hat worn by Royal Air Force officers is nearly a subversion of the trope. Small and with horribly bent edges that sag downwards, it harks back to the time that all RAF officers were pilots and their hats were much abused, normally stuffed away in some pocket and thus scuffed and worn. In all other words, a mess, and in contrast to the hats worn by other ranks which are rather smart.