Angel Beats!: Yuri wears one while issuing commands at headquarters, Naoi has a nice one too, as part of his uniform, and Angel wore one in episode 7 in the garden.
Angel Blade: Phantom Lady's helmet is her most distinctive feature. She looks suspiciously like the heroine's mother without it.
The Holy Roman Empire in Axis Powers Hetalia. Prussia has been seen with one during the War of Austrian Succession. Turkey also sports one alongside a Cool Mask. Turkish Republic of Northern Cyprus, Sealand, and Egypt (if a keffiyeh counts) normally wear hats, and Liechtenstein, Sweden, Hungary, Poland, Switzerland, Finland, Norway, and Denmark have all had character designs with hats, though not all necessarily nice ones.
Generally speaking the mafia place value on hats which, while not particularly flashy, are still quite nice hats. In the scene where Firo gets his Fedora, we also see Isaac and Miria buy off a huge stash of ludicrous hats and helmets.
Black Butler is full of nice hats. Considering the time period the series takes place in, hats were a must for men, women, and children when leaving the house, at least for the wealthy.
Ciel wears a tophat whenever he goes out, which often has a ribbon or some other decoration on it. The most memorable hat is probably the one he had to wear while crossdressing which included a ribbon, bow, and many flowers. There's also the adorable paperboy hat Ciel wears when he goes undercover.
Oh, and the hat from the Curry episode. How one can wear it without it falling off is anyone's guess. It must involve several hairpins and the will of God.
Undertaker's hat is also rather nice. It has that nifty ribbon thing flowing down off the top.
Chuya's iconic hat. (Dazai doesn't agree that it's nice.)
Ranpo wears something like a paperboy's hat.
Q has a cute little hat that sits at an angle on his head.
Steinbeck's hat completes his farm-boy look.
Mitchell, likewise, wears a wide-brimmed hat that goes well with her Southern Belle look.
Fyodor has a fluffy hat that he seems to be somewhat fond of. (Unlike with Chuya, Dazai actually seems to like his hat. He wore it once.)
He never wears it on his head, but Kenji has a straw hat that usually hangs around his neck. Lucy compliments it at one point and later wears it herself briefly.
Genzo Wakabayashi, the SGGK (Super Great Goalkeeper) from Captain Tsubasa always wears his trademark red cap with a green G on it. (Or a black G in Road to 2002). Whenever he puts on more official uniforms, he also puts on other caps in matching colors; i.e., in the Road to 2002 anime he wears the official black GK outfit, including a REALLY nice black cap. As an adult, he also sometimes wears a white cap with a dark green G.
Wakabayashi's rival Ken Wakashimazu used to wear a white cap, but ditched it in the second part of the series. Unlike Wakabayashi, he does not wear caps when in National Team uniforms.
Cardcaptor Sakura has some nice hats from time to time. Most of these are courtesy of Tomoyo Daidouji, who appoints herself Sakura's personal fashion designer, and often themes Sakura's dresses around the Clow Card she's currently fighting.
Mr. Tiellagory of Le Chevalier d'Eon has a sweet hat with a nice big feather in it. Durand is the first character to damage it in a Sword Fight, only to find that damaging the Cool Old Guy's hat is often followed by swift humiliation.
Later in the series, while fighting a pack of magically enraged dogs, a shot cuts to Tiellagory holding his hat, surround by them. When another character rushed to his aid, he turns to them and says, "My hat..." following which the dogs fall down dead.
In one episode of Digimon Adventure 02 Takeru "TK" Takaishi's signature hat becomes an indicator of his state of mind when he crumples it and throws it to the ground in anger — disturbing Iori/Cody who, prior to that moment, saw Takeru as a Cheerful Child — just before he storms off on his own and physically attacks the Digimon Emperor. Later, once his anger had abated and his usual affable persona had been mostly restored, a still visibly shaken Iori gives him his hat back. About the only other time he takes it off is toward the end of the series as a solemn gesture of respect and mourning during the death via Heroic Sacrifice of Yukio Oikawa.
Tomoki/Tommy from Digimon Frontier wears an orange hat 1.5 times the size of his head. In real life, that hat would be ridiculously ugly. He takes it off several times in the series. Every character except Junpei/JP wears a hat or some type of headgear. (Takuya — goggle hat, Koji — bandana, Koichi — baseball cap (in flashback scenes), Izumi/Zoe — purple cat-eared beanie)
And from Hiro Mashima's earlier work, Rave Master, we have Deep Snow and his ginormous hat that is in the realms of "Pope or Not Pope."
The H-manga Fudotei Student Academy (by Unagimaru) plays with this trope hilariously, as the confident, powerful, and dictatorial student council president becomes incredibly shy and meek when her German Officer-style hat is removed. Fortunately, the protagonist falls in love with both sides of her, so it's okay.
Asuka wears a rather impressive sun visor in races, complete with pink hearts on each side in the first two series (and in the first episode of ZERO). Miki, the series' resident Wrench Wench, wears a nice cap with her name on it.
Gudelhian wears a cowboy hat most of the time when he's not racing.
In Galaxy Express 999, both Maetel and Tetsuro wear distinctive hats. Maetel's is a tall, almost cylindrical fur hat, Tetsuro's is low, rumpled, and very wide-brimmed. Tetsuro's hat was made by the mother of Tochiro, who wears a similar hat.
In episodes 4 and 5 Albert wears a nice pirate hat.
Kuroudo "Doctor Jackal" Akabane from Get Backers always wears a wide-brimmed hat with a cut in the brim. All damage Kuroudo's clothing ever sustains quickly regenerates except for that one cool cut. The creator lampshades this by mentioning how the hat brim (along with his hair and coat) seem to get longer every time he shows up.
Zangetsu the Midday from Giant Robo: The Day The Earth Stood Still only appears for about ten or fifteen minutes, in the final episode. However, fans of the show have taken quite a liking to him, if only because of his nice hat.
Quite a few people were concerned that, three hundred years into the future, the United States Navy may tailor fanciful hats as part of an officer's standard uniform, as evidenced in Gundam 00.
Van from GUN×SWORD sports a nice hat with a Jigen notch, a ring on one side (which he spins the hat around with to indicate its Humongous Mecha time), and is apparently pretty precious to him, considering we never see him without it.
Wannyuudou has an awesome wide-brimmed hat. In the first two seasons, he's rarely seen without it — which is understandable since he's bald underneath. In the third season, Ai's helpers are usually seen at school in disguise, so the hat appears less often.
Baron Will A. Zeppeli in Part 1 has a rather awesome checkered top hat. After his death in the Room of Dragon Decapitation, Speedwagon wears it for the rest of the part. In the second part, Zeppelli's descendant Caesar has apparently inherited the hat, though he sadly ditches it after his introduction.
By the third part, both Joseph and his grandson Jotaro have picked up nice hats — Joseph has a tan-colored Panama that makes him look like Indiana Jones, while Jotaro's biker's cap is so much a part of his character that Araki deliberately drew it so one can't tell where the hat ends and his head begins. In the anime adaptation of the fight against Terence D'Arby, the hat is actually drawn with little "wings" on the back that mimic Jotaro's wavy hair.
And nearly everybody in Part 7 Steel Ball Run has a hat of some sort. Most notably, Gyro Zeppeli's cowboy hat, and Johnny's hat with a horseshoe adorned on the front.
Every Jojo fan knows that Part 2 Joseph is the king of nice hats: in one of the chapter covers he wears at least three at the same time◊. Joseph's "hat stack" is something of a meme within the fandom. Part 2 also features Joseph's goggle-and-aviator-helmet from his trip to Mexico, as well as the ushanka he picks up in Europe.
Josuke from Part 8 has a 'dixie cup' style sailor hat with stripes and a tassel. He was even found wearing it after being buried in the Wall Eyes. We later find out it was Yoshikage Kira's hat, fitting with the sailor theme clothing they wore.
Uni wears the same Nice Hat◊ that her grandmother, Luce, wore.
When Tsuna and his guardians get blasted ten years into the future, the Varia have another illusionist by the name of Fran who is wearing a frog-shaped hat that is so large he can't even get his arms over it. We learn later when the Varia first went to recruit him, he's always had an odd taste in hats, as he was wearing a giant berry-shaped one...
Kemono Friends: The main heroine Kaban wears a tattered pith hat with a feather in it. This feather is what makes Lucky Beast respond to her with the Mirai recordings.
Kobato. 's hat (and outfit) changes every day mysteriously (considering she has little money and no possessions) and there are hints that Kobato should never take off her hat for reasons unknown as of yet. It's still a mystery in the manga, but the anime makes up a very good one: the hats cover a small magical crown on her head, which is evidence that Kobato has been Dead All Along.
Vita's Knight Clothing has a stylish red hat complete with stuffed undead bunny heads on each side, and quicklygot serious when Nanoha damaged it.
That same incident provided the first clue that the Wolkenritter aren't all bad, when Signum shows up and the first thing she does is to repair Vita's hat. The hat was a gift from their master, and they all love her very much.
Shamal's Knight Clothing has an equally-stylish green one with something of a Middle-Eastern flair.
Himari's hat in Mawaru-Penguindrum is an impressive piece penguin-themed piece of headgear. It's also a character in its own right: a sprit named the Princess of the Crystal resides it it, and she kick-starts the plot by bringing Himari back from the dead and then commanding her brothers to find the "Penguindrum" if they want her to keep Himari alive.
Yoite from Nabari no Ou has a pretty nice gatsby. Enough that quite a few people recognize it as "The Hat Anime." Reportedly, Yoite's hat is what caused many fans to begin the series in the first place.
In My Hero Academia, a hat is part of the school uniform of Shiketsu High, students are even required to wear it at all times to signify how their actions reflect their school's name.
Since it is a pirate manga/anime, there are a lot of Nice Hats in One Piece—
Monkey D. Luffy wears the straw hat Shanks gave him that once belonged to Gold Roger. One of the most memorable early moments was when he put it on Nami's head before storming off to liberate her island.
This hat is so central that both himself and his crew is named after it: "Straw Hat Luffy" and "The Straw Hats".
This is a bit of a subversion, as it's a very ordinary-looking straw hat that doesn't do anything special (as far as we know), and Luffy values it for sentimental reasons. Still, god help you if you damage it.
Apart from the Strawhat, Nami is seen a wearing cowboy hat in mutiple color spreads but doesn't actually wear any headgear in cannon till Whole Cake Island where she dons a small black brimmed hat before losing it in the Seducing Woods.
Usopp wears a bandanna over his head like Zoro, which he often adorn with his signature goggles. After the timeskip, Usopp wears a big low brim hat which was is unique but not striking. In Dressrosa he wears a much more cooler orange pilot's cap, Usopp is very rarely seen without any headgear (even more than Luffy).
Sanji rocks a stetson in One Piece Film: Strong World and wears a cowboy hat in a few color spreads. The only cannon headgear he actual wears is the ball hat in Groggy Ring (which he hated) and the iron mask he wore while imprisoned as a kid.
Tony Tony Chopper has a pink top hat which was given to him as a reward by Hiluluk after the two had a fight since Chopper "proved to be a man" causing the reindeer to cry. The hat is bigger than his head and his antlers can somehow poke through (After the time skip, he put a blue cover over his top hat that has antler holes AND ear holes).
Robin first appeared with a white cowboy hat and later a purple one
Brook has a top hat that he wears ON TOP OF HIS AFRO - and after the Time Skip, he upgrades to a crown.
Rob Lucci, uses a distinctive top hat that he never removes, even while on a secret mission. Likely influenced by Sting from Guns and Roses.
Kaku's baseball cap. His CP9 uniform even comes with a black version.
Admiral Sengoku, who has a whole seagull on top of his hat, presumably stuffed, although the author is crazy enough that it might be alive and calling the shots.
All but two of the Eleven Supernovas have very distinctive headgear. Kidd has a pair of studded goggles, Law has a fur hat, Bonney has a turban-like hat, Bege has a mafia-style cowboy hat, Apoo sports a pair of headphones, Killer has a full head sports-helmet looking thing while X. Drake wears a white-plumed cocked hat AND a mask.
Ace has a cool hat, too. Fittingly, so did Luffy and Ace's 'brother' Sabo when they were young. It was last seen in a Dead Hat Shot.
He's later revealed to still be alive, and indeed still rocking the same (or at least a very similar) hat.
Charlotte Linlin (better known as Big Mom) has a pink bicorne hat with a skull and cross-swords design on it. It looks fairly nice, but it's also alive, called Napoleon, made of a piece of her own soul and can transform into a giant cutlass.
Paradise Kiss Isabella and George often include hats in their many outfits. George usually settles for cowboy hats, while Isabella wears spectacular picture hats with ribbons and flowers most of the time.
Hero Ash has had his hat stolen by his Aipom, a Mankey that he later caught as a Primeape, and his own Pikachu in the second movie (in order to make Ash follow him). The very first hat he is seen with was said to be earned by tirelessly sending around two hundred coupons to win an official Pokémon League contest, and the other two were given to him by his mom. He has a habit of turning his hat backwards when he's about to get dangerous. In fact, this hat is so Nice it has its own Bulbapedia article. In the The Electric Tale of Pikachu manga, Misty used Ash's hat as the goal for the Cerulean Gym battle... against his will. Then it got sillier.
In the anime, Nando and Riley both have very nice hats.
Pokémon usually don't have Nice Hats, but Tyson's Meowth (the ace of his team) had a cowboy hat (with matching boots). Team Rocket's Meowth considered getting a hat of his own while watching it battle, being so impressed with its power.
Ruby has a very nice hat, though odd looking for a beanie, that he rarely takes off. It hides his scar.
Red also counts. He had his hat on while swimming, taking a bath, and even when he's literally half-naked in FRLG. It never fell off even in the most dire of consequences - except in the last part of FRLG, because the writer wanted both Pikachu to return it in the Emerald Saga.
There is also Yellow's hat, which she was given by Blue to disguise her identity and had feathers from Ho-oh and Lugia, which came in handy much later.
Just like their game counterparts, other main character also have nice hats. Crystal has that weird bowl-shaped hat and Green/Blue has Leaf's nice hat after they were updated to match their game counterpart. Gold has his ball cap, Ruby has his weird hat that appears to be his hair (it isn't), Sapphire has her bandanna, Diamond has his hat, and Platinum has her beanie.
The various other Pokémon manga don't fall short of them either. Phantom Thief Pokémon 7 has Rocco's top hat. Pokémon RéBURST has Ryouga's signature hat (of which he keeps a huge amount of spares), Yappy's straw hat, and Sabin's witch-like hat.
In The Prince of Tennis, one of Ryoma's trademarks is his Nice White Cap. Sanada has his contrasting Nice Black Cap, Kaidoh uses a Nice Bandanna (or several), Wakato from the anime also uses a Nice White Cap, and the Kisarazu twins started using Nice Headgear (a white cap for Ryo, a red headband for Atsushi) after an accidental Twin Switch.
Ranma ˝ has several instances of this. Shampoo has her odango covers. Multiple characters have headbands or bandanas of some kind. In fact, Ryoga wears several layers of bandanas, and will often attack with them. Ranma's pig tail is bound with the whisker of a dragon, which when boiled can produce a broth to regrow hair. Unfortunately for men who already have good hair, this will result in their hair growing until it all falls out, unless bound with said whisker.
Jin of Samurai Champloo often wears a nice kasa. He uses it to demonstrate just how badass he is by tossing it into the air before a fight, invariably finishing his foe(s) in time to catch it before it falls below chest level.
Yuki from School-Live! has a cute cat-ear shaped cat. It, along with her backpack with angel-wings on it, signifies her as quite immature for a high schooler. In the final episode of the anime she gives up her hat to bury with Taromaru, which goes along with her becoming more competent and becoming less delusional.In the manga she keeps her hat even after leaving the school. As a part of being a deconstruction of the CloudCuckoolanderGenki Girl archetype, her hat and odd personality caused her to be bullied prior to the Zombie Apocalypse and she had no friends besides her teacher Megu-nee.
Some of the headgear of the soldiers of Seirei no Moriboto is quite impressive, in both looks and elegance.
Hecate of Shakugan no Shana is lookin' kinda stylish, but where would she be without that huge hat?
Knuckles the Echidna of Sonic the Hedgehog fame randomly got a Nice Hat in the Sonic OVA. For the sadness of many (okay, some), the OVA is the only time where he wears the hat. The hat also made an appearance in the Archie comics, and was worn by an ancestor of his. He only wears it in stories set in a future timeline; according to a letter page it's because he doesn't want it to get damaged.
In Star Driver, Takuto's cybody Tauburn is a rare example of a mecha with a nice hat. So does Reiji's Reshbal in a similar fashion.
Strike Witches: While it's not something she ever wears in the anime itself, Yoshika Miyafuji has been portrayed in the occasional bonus art and some◊ toys with a nice sailor's cap. It also appears briefly (0:50 to 0:55) in the Over Sky ED.
Given that they have the traditional detective ensemble, the four girls of Milky Holmes in Tantei Opera Milky Holmes have colorful deerstalker caps on their outfits. Bonus points to Nero, who wears a similar hat as part of her school uniform.
How nice is Kotetsu's hat in Tiger & Bunny? So nice that the fandom rejoiced the moment Sunrise announced that they'd be selling them.
In Tokyo Babylon Subaru is always seen in somewhat extravagant hats, all proudly picked out by his sister Hokuto.
Lala of To Love-Ru certainly has a Nice Hat. It has wings. It also happens to be an intelligent robot that functions as her clothing.
Any high-ranking person in Trinity Blood, most notably the vampire Empress.
The title character has a nice Cavalier-style hat with a neat mother-of-pearl pin.
The trope title is used as an actual line when Action Girl Leila sees the portrait of Carmilla, whose hat◊ resembles a large red sausage placed on her head, made of part of her hair and odd, cap-like things on the end.
The outrageous headgear used by both heroes and villains in Violinist of Hameln (manga and anime)—
Hamel's pointy, wide-brimmed feather hat is a huge plot point, even, since he hides a small horn — the only proof of his demon blood — under it. The hat's removal is usually followed by a Crowning Moment of Awesome, a Crowning Moment of Heartwarming, or a horrible, horrible mob scene.
Raiel's hat is even more epic, but it just underlines his usual dorkery. Sizer's dragon helmet is awesome. And Tron wears a very frugal crown. Even Flute's hat becomes iconic. This manga knows about nice hats, evidently.
Slyly subverted in Yotsuba&!, in that Yotsuba's most awesome adventures are signaled by her putting on a hat that can be charitably described as a pudding with a brim. Ena's hat, seen occasionally, looks even more like a pudding, without a brim. Not at all nice hats.
A minor joke among the Yu-Gi-Oh! fandom: when the monster called Cosmo Queen is played, it is greeted with "Nice hat."
Less memetic and more nice: the Dark Magician family all wear stylish headgear.