All of this is somewhat Truth in Television, since the Jägers (and the GG Verse in general) have heavily exaggerated elements of Prussia in their role and backstory: Prussia, the kingdom that brought you this. Even the eagle on top of that hat is wearing a hat. Prussian general Gerhardt "Vorwarts!" von Blücher, having helped win the Battle of Waterloo, donned Napoleon's captured hat, thus making clear to all the world that after 23 years of constant war, it was Really Truly All Over.
Maxim goes hatless for some time after giving his hat to Lars. Then comes the side story, "Elsewhere: Maxim Buys A Hat", where he sets out to get a new one from "Ol' Man Death! — De Big Guy Himself!"
Maxim: A Hat iz a badge of honor! A Trophy vat must be plucked from off de head of a vorthy enemy!
Oggie: Yah. Vun who happen to gots hyu same head size.
A throw- er, blowaway character with the radio tuner hat is listed in the vol. 7 cast page only as "The Idiot in an Awesome Hat". Lord Selnikov's hat is pretty epic too, though.
From the Girl Genius card game The Works, we have General Cannonhat and his Amazing Cannon Hat. His epaulets even have little hands to plug his ears!
Gilgamesh's hat takes the cake, though. Easily. It has wings, spikes, tubes, his name in big letters with "Schmott Guy!" underneath and a burneron top. Possibly the Nicest Hat ever, given by Jagers as a sign of respect. It even has a name, according to the cast page: Gil's Fabulous Hat. And someone whose job it is to take care of it.
The Continentals: Set in Victorian England 1889, the entire cast of characters in this steampunk murder, mystery, scifi adventure webcomic wear a variety of fashionable headwear of the day from top hats to derbys, etc. The most eyecatchingly noticeable would be the gender bending, cross dressing adventress Lady Fiona Fiziwigg, whose prominent and somewhat oversized top hats have earned her the nickname "her tophattedness" by the comics readers. Find it here.
Also, Nash Straw/Reynold Strom's wide-brimmed black hat, which complements his Badass Longcoat nicely. He even gets a version with Hereti-Corp's logo when he's working for them. And his rebel soldier counterpart in 4U City has one too.
In San Three Kingdoms Comic, which uses the Dynasty Warriors character models, Cao Cao's hat has a small duck atop it, and is referred to as "the Duck Hat". One of his advisors, Guo Jia, wears a Baozi (Meat Bun) Hat. Both hats possess the power of hypnosis, but Guo Jia's is apparently stronger.
PvP occasionally features the 'Gaming Fez', a Fez which makes you awesome at (virtually) any game BECAUSE the Fez makes you look awesome. Only the remarkably thick-headed Skull the Troll has proven able to handle its awesome, shining power, while anyone else who've donned it soon became drunk on its power...
Freefall's Florence Ambrose receives a gold cloth hat that proves to be quite popular with robots for its transponder-blocking qualities: starting here.
In El Goonish Shive, Sarah's beret is so cute/awesome that the principal allows her to wear it despite it being against the school dress code. (Also, author Dan Shive is quite aware of the importance of hats, as seen here.)
The Brigade du Chapeau from Kukuburi consists of a gang of strange creatures wearing hats with special abilities (such as Rendo's Hammerspace bowler hat).
The six-armed Spinnerette!, after a fat and gravity-powered villainess mocks her deodorant bill, angrily declares that "If I were going to insult you, I wouldn't go for the obvious. I'd make fun of ... your stupid HAT!" The villainess is outraged - you can insult her, but no one insults traditional Alpine hats.
Lowping, the Gnome rogue in Flintlocke's Guide to Azeroth, ninja looted an epic mage hat, twice from Bloodrose, the group's mage. One of his most recurrent stock phrases (being a bot) is "I lewt da hat".
In Bird Boy the outfits worn by Bali's tribe include painted Native American style animal headdresses. Bali's is a bird (hence the title) with a beak so big it often hides most of his face. And it's pretty cool.
ROSCOE SCAGGS wears a strange yet impressive mix of wizard hat and winter cap.
Valentine from Cloudscratcher. Comes with being a Smooth Criminal homage.