Most of the Catholic hierarchy in some form has a cool hat they wear, with the bishops, archbishops, and cardinals all having their own style of hat.
The papal camauro: Pope Benedict looked a lot less intimidating (and a bit less like Palpatine) in a Santa hat. Camauro is the actual name for a santa hat, as St. Nicholas of Myra was a bishop way back when.
The Queen. Duh. Every time she appears in public, it seems everyone wants to see what new Nice Hat she has.
The Imperial State Crown contains over 3,000 jewels, including a 317-carat diamond. It's Awesome but Impractical; the damn thing apparently weighs a ton and is murder on your royal neck.note "Uneasy lies the head that wears the crown" indeed. The St. Edwards Crown, which is the one normally used at coronations, is heavier.
Inverted by Queen Vicky, who after becoming a widow decided that her crowns were too nice (and heavy), and commissoned a small cute one in its stead.
Date Masamune is not just known for his one eye which requires him an Eyepatch of Power. He's also known for his snazzy helmet with the crescent moon piece on the top of it. This helmet almost always appears alongside Masamune whenever he is featured in other media.
Also from the same era, Naoe Kanetsugu, retainer of the Uesugi, had a helmet which featured not only metal crests and 'wings,' but also the entire kanji for the word 'love'◊ emblazoned on the top. The word alone is very nearly as large as his head would have been.
The various Chinese dynasties, being a multi-tiered bureaucracy from hell, featured funky-looking hats (and outfits) of all shapes and colors. Special mention goes to the ladies of the court, who would also wear fake hair shaped into a variety of mind-boggling shapes.
The Akha people of Southeast Asia wear ornate headdresses nearly everywhere they go: photos.
Terry Pratchett is often pictured in the covers of his books wearing a rather nifty black hat. It is apparently a form of disguise as without it he is, in his own words, just any other bald man with a beard. Indeed Moist von Lipwig relies on a similar technique in his Discworld books.
He replaced it with a top hat while promoting Dodger and was apparently taken enough to keep wearing it for a while afterwards. In promotional material for Raising Steam, he sports a stationmaster's cap.
Dr. Gunther von Hagens is rarely seen without his black fedora, and has worn it while performing public dissections.
In North America, the wearing of men's hats as not only fashion but standard business and formal attire, began to fade during the early 1960s. One of the hallmark moments often cited for this decline in the various hats' popularity is the inauguration of President John F. Kennedy in January of 1961. Though Kennedy wore a full formal morning suit, including top hat, to his inauguration speech, he was most famously seen on television without a hat while delivering his speech. American men's fashion began to become more relaxed as the 1960s went on and the hat, be it fedora (of Asskicking!) or trilby, boater or bowler, faded out of fashion to be replaced with naught but the baseball cap as informal attire. Though the actual impact of a new, young, and fashionable President addressing the public sans-hat (an inversion of The Red Stapler) has been debated, the popularity of the men's hat has not returned in North America or elsewhere in the Western world.
The hats for women, most prevalently in the South, could get pretty wild and wacky, particularly in late 19th and 20th centuries (this tradition is kept alive to this day by some, though, as noted below). In the early days of movie theaters, one common slide you'd see where today you'd see "don't smoke, don't talk, turn cell phones off, throw trash in the receptacles, fire exits are at the sides", they'd have "Ladies, kindly remove your hats", maybe even accompanied by a cartoon of some poor sod's view being obstructed by, say, a two-foot-tall pineapple-wielding monster. (As an aside, another common slide in that era would also remind people "Don't Spit on the Floor — Remember the Johnstown Flood.").
Averted by Fidel Castro, who is known for his iconic yet understated military cloth cap, although some would hold this to be a Nice Hat of it's own for that very reason.
The fondness of military dictators (Mussolini, Pinochet, Amin, etc.) for huge peaked caps has led to them being called "dictator caps".
Mussolini is usually associated with a different, peak-less cap, both because he was not a military dictator and because it was the rest hat of the Bersaglieri, Italy's elite infantry in which he served during World War I.
Tennis players are often fond of using Nice Baseball Caps when playing. The one who began the trend was Jim Courier, with his Nice White Cap. Kind of a Justified Trope for the absolutely asinine heat in some courts, especially during the Australian Grand Slam (50°C?! HOLY SHIT!)
It has become quite popular, The Milliner has made replicas which sell for $179.
African American women are all expected to have a Nice Hat that they can wear to church (as women were supposed to have their heads covered; this was just taken to great levels in Southern Baptist churches). They are often even called "crowns".
In fact, a book called Crowns is all about these hats and the ladies who wear them.
The top hat Hugh Jackman wears in the 2009 Oscars "The Musical" musical number... or just about anything he wears, actually.
Not hard at all, but the stovepipe was still just so him.
As Lisa Simpson once described it: "America's greatest citizen summed up in one piece of clothing."
Disney's Hollywood Studios in Orlando has a massive version of the Sorcerer's Hat (from the Fantasia version of The Sorcerer's Apprentice) over a pair of Mickey Ears.
What very few people know is that the Royal Ascot horse races are actually a horse racing event and not, as one might easily be mistaken, the worlds most important annual fashion convention for crazy hats.
He also owned an incredibly epic tiara◊, specifically made to outdo the Pope's. He apparently never actually wore it, likely because it was so huge that his spine would have crumbled under the weight.
Boxing historian and author Bert Randolph Sugar was rarely seen without his trademark fedora (and big cigar).
the late Isabella Blow was never photographed without a hat, and was in fact an early mentor/patron of Philip Treacy- she even got a museum exhibit dedicated to her headgear.
Florida Rep. Frederica Wilson, who wants the House rules amended to allow Nice Hats on the floor.
Also, former Chicago alderman Dorothy Tillman was also known for her hats.
Swiss physicist, inventor and explorer Auguste Piccard◊, who inspired Hergé the character of Cuthbert Calculus in the Tintin series.
The Ushanka has become so synonymous with Reds with Rockets that it's become hard to imagine any Russian soldier not wearing it in winter.
Famed USMC sniper Carlos Hathcock was known as Long Tr'ang, or "White Feather", for wearing a feather on his hat. While the image itself might seem cliched, remember that this is a man who once shot a feared enemy sniper through his rifle's scope, performed a non-lethal shot on a courier on a bicycle from a mile away with a machine gun, wiped out a company of North Vietnamese soldiers along with his spotter in an isolated valley, crawled through an open field patrolled by enemies to assassinate a North Vietnamese general in a heavily guarded mansion, and severely burned himself rescuing several fellow Marines from a burning APC, after an exploding mine threw him off said APC. Definitely lots of cool to go with the hat there.
Instead of the mortarboard hats used at graduations in a lot of English-speaking countries, Scandinavians and Finns graduate from high school wearing these◊, which are often decorated according to the program/school you graduated from.
Princess Beatrice◊ from the wedding of Prince William and Kate Middleton. It is headgear not to be missed.
It got nearly 20,000 fans on Facebook within hours.
The Chaperon (basically Medieval Europe's answer to the Turban) started off rather utilitarian and became increasingly complex over time. Even today, the exact nature of "its complicated construction is often misunderstood". Most people familiar with that era of history would recognize it as those ridiculous hats worn in Renaissance paintings. Its probably the inspiration for Quirrel's turban.
LSU's American Football team's head coach Les "Mad Hatter" Miles and his white caps that he wears while he's coaching. He's known for some other eccentricities, as well, most notably eating a sample of the grass from the field before each game.
American Football helmets have some nice designs.
Oh well if we're counting sporting helmets then hockey goalie helmets are never short in the awesome department.
On the football thread, Packers fans wear Cheeseheads at Packer games. Yes, yellow foam cut to look like cheese. Go to any Packer game and you're bound to spot one (even away games).
The Chinese People's Liberation Army Marine Corps. While their hats by themselves are just unremarkable woolen tuque caps, they always have a pair of goggles worn over their head, and never over their eyes. ◊, ◊, ◊. Even if they require some sort of eye protection, they always keep the goggles on their head and instead opting for their own pair of sunglasses or shooting glasses. One might suspect if the goggles are simply there for looks, playing the Goggles Do Nothing trope straight.
Neither German singer Udo Lindenberg nor German artist Joseph Beuys are thinkable without their hats. (To the point that a cartoon exists titled (approximately) "Beuys and Lindenberg swap their hats after a drunken night.")
That snappy-looking hat that seems common to military drill instructors, park rangers, and the occasional sheriff of small towns... whatever the hell you call it.
"Lenna"◊, a photo of Swedish model Lena Söderberg used as a standard test image for image processing algorithms is notable for the hat. Yes, the photo appeared in Playboy. Yes, the hat and the boots are the only things she is wearing in the full image.
England wicketkeeper Jack Russell always wore the same plant-pot-like hat when keeping wicket. By the end of his career, it was very tatty indeed, but he refused to play for anyone who wouldn't let him wear it.
The Bersaglieri, Italy's elite troops, have two. The first is the vaira◊, originally worn as protection from swords (the Bersaglieri were meant to charge against cavalry, so they needed it) and shield their eyes from the sun while they shot their enemies (their name is Italian for 'sharpshooter'), and is currently used as part of their dress uniform. The other is a red fez, first adopted when the Zuavi (French colonial light infantry), at the time considered the best infantry in the world, saw them charging and routing a large Russian cavalry force in the Crimean War and decided to show their admiration for that feat.
Benito Mussolini, having served in World War I as a Bersagliere, wore his fez whenever he could get away with it to remind everyone that he wasn't just a braggart.