Sokka at one point picks up a hat shaped like a wolf's head.
Even though she was a background character appearing only once with one line of dialogue, this woman◊ clearly knows how to accessorize.
Sokka's detective hat from "Avatar Day".
Fievel Mousekowitz' hat from An American Tail. It's apparently passed down through the family line (As explained by his father), and so iconic that possession of it is able to convince Papa (Who had spent the movie refusing to admit his son might have survived being thrown overboard and getting his hope up) that Fievel is alive. It somehow gains the ability to be unfolded into a cowboy hat in the sequel.
In Dragon Hunters, Gwizdo is usually shown wearing his aviator's cap, complete with goggles.
Darkwing Duck has a real nice hat, though most of the residents of St. Canard disagree. And of course his Evil Counterpart Negaduck has the same hat.
An episode or two had an alien race of nice hats. Although, considering they were trying to take over the world as mind-control parasites, I'm not so sure "nice" really applies.
The evil aliens were set on Grand Theft Me. The good aliens were very nice hats, and their leader, Klattuu-tu, is a hat on par with the Pope's hat.
Donald Duck loves his sailor hat; anyone taking it from him, or damaging it in the slightest will soon be suffering Unstoppable Rage from Don.
Chowder has a frickin' nice hat (or "vacation home" as it is known by recurring character Chestnut).
The 1960 Paramount cartoon Top Cat (by Famous, the studio that produced Casper and such) features a cat who sings about the paramount importance of wearing the right kind of hat. As he demonstrates, if you want to succeed in life, all else pales to unimportance.
There's also Hokey Wolf and his sidekick Ding-A-Ling.
An episode of Duck Dodgers had nearly the entire cast mistake a brain probe on the main character's head for an awesome hat. (Making Dr. I.Q. High, who had a pretty Nice Hat of his own, rather jealous.) Even the enemies who planted the probe on him mistook it for a cool hat.
Sergeant Slaughter seems awfully fond of his drill sergeant hat in G.I. Joe. In one episode, a Cobra grunt hits him over the head with a crowbar, making him upset... Not because it hurt him, but because it dented the hat. (Slaughter then knocks the grunt out with a head-butt before putting it back on.)
The magic portal hat(s) in the Pixar short "Presto!" Not one awesome hat, but two!
In The Venture Bros., Dr. Girlfriend originally wore a Nice Hat based on the one worn by Jackie Kennedy Onassis, and an ensemble to match. Ironically, she had no idea who that was. (In later seasons, she got ditched it in favor of a Cool Crown.)
All of the main four characters of South Park wear hats (though one would be hard pressed to consider them particularly "nice"). The episode, "Follow That Egg", however, has the following exchange:
Kyle: Do you really think my hat is stupid?
Stan: As a matter of fact... I think it is the nicest hat I have ever known.
Animals Close-Up With A Wide-Angle Lens Wearing Hats
Like Professor Layton, Edd from Ed, Edd n Eddy is never seen without his black stocking cap with two white stripes going down it. Fans are very curious about what's under it.
Although, Edd's hat has come out a few times, and Edd has sometimes wore other things on his head (sometimes not removing his cap), with the most noble example being The Movie. Fans believed that they would finally see what would be under Edd's hat, but Ed's big fat head blocked the scene.
Kevin may fit this trope better than Professor Layton or Edd. In the first few seasons of the show, Kevin never, ever removed his hat. Even to take a bath.
Samurai Jack sometimes wears a handmade straw hat which looks rather cool. It tends to be destroyed often (along with the rest of his outfit, more often than not), but he knows how to make replacements.
The Mayor from The Powerpuff Girls has a very nice hat, and woe be unto he who steals it from him.
Buttercup: "But we don't get to fight crime anymore!" Mayor: "I don't care." Bubbles: "He's turned your office into a pig stye! Literally!" Mayor: "I don't care." Blossom: "He's tarnishing the image of what it means to be mayor!" Mayor: "I don't care." Ms. Bellum: "He's wearing your hat." Mayor: "...!!!!!"
Lampshaded somewhat during the "Kamp Krusty" episode of The Simpsons when Bart is listing the atrocities that were suffered at the camp.
Bart: And one of the kids was eaten by a bear! Krusty: OH MY GOD! (sobs uncontrollably) Bart: Well, it really only ate his hat. Krusty: Was it a Nice Hat? Bart: Oh yeah. Krusty: OH MY GOD! (sobs uncontrollably)
Marge: Your father can be surprisingly sensitive. Remember when I giggled at his Sherlock Holmes hat? He sulked for a week and then closed his detective agency.
Hijitus, a cartoon series very popular in Argentina, Uruguay and Paraguay and emitted in Argentina between 1967 and 1974 and credited as the first serialized Latin-American cartoon, starred the eponymous character, a homeless boy with an unraveled top hat (his "sombreritus") which allowed him to transform into "Super Hijitus".
Doug Dimmadome (owner of the Dimmesdale Dimmadome) of The Fairly Oddparents has a hat so nice, it can't always been seen in full; some episodes have it extend past the top of the screen regardless of how far away from the camera he is.
Of course, there's Timmy's hat, and the floaty crowny things.
It is worth noting that, midway through the live-action movie, Timmy loses his hat during his date with Tootie, but she gets him a pink fedora to replace it.
Numbuh 5 (a.k.a Abigal Lincoln or just "Abby") from Codename: Kids Next Door rarely takes off her red cap (due to the fact it was a present from her older sister before her Face-Heel Turn.) The only time she does is mostly to use it as weapon.
Truthfully, she lost the original hat in "Operation: L.I.C.E." when raiding the Delightful Children's manor for nacho chips and replaced it with an identical one. This issue was not addressed again.
There is also the KND Supreme Leader, Numbuh 362, and her colander-helmet of power. Any headgear that include scimitars must fall under this trope.
Raphael: Nice hats! Michaelangelo: Yeah, we thought so, too. Donatello: Say what you will about the Foot, but they do not skimp on the headgear.
Twister in Rocket Power. He's barely recognizable without his hat and had a whole episode when he lost it.
Dale Gribble refuses to take off his hat in King of the Hill. He was hatless in one episode when he's working at an adhesives company when he can't exterminate anymore.
Hank's pimp hat in "Ho Yeah!"
Where on Earth Is Carmen Sandiego? Wherever she is, she's wearing a kicking fedora. (Seeing as she's the type of thief who wants the cops to know she did it, she has been known to leave the hat at the scene of her crimes as a "calling card".)
Star Wars: The Clone Wars introduces the elite Duros bounty hunter Cad Bane, in the running for the position of the biggest badass introduced in the show. Naturally, this comes complete with a Badass Longcoat and a sweet wide-brimmed cowboy hat.
After evading capture by the jedi, he sets out his accomplices to find guns and a ship while he finds... yeah, a cool hat replacement. One of his accomplices tells him off for attracting attention, but he's clearly too cool to care.
Serious Business indeed. In a recent episode, he kills another bounty hunter because he wore a hat identical to his old one (and then took it for himself, of course). Cad Bane clearly thinks it's a reallyNice Hat.
Secret Squirrel has a pretty nice hat himself—and he's the only one who can see through it. Penny wears one herself on the occasion when she goes on her own missions.
The Nightmare Before Christmas: Sandy Claws' red hat. Not awesome, you say? Consider that out of all the things blown up by the anti-aircraft shells, the hat was the only thing to remain intact. That is one Bad Ass hat.
His counterpart on The Batman wore a number of hats too, often as part of a costume. He was visibly upset in a season 5 episode when his sea captain hat is blown off during a getaway. Later in the episode he dressed as a miner with matching hat.
In Phineas and Ferb, Perry the Platypus wears a fedora on his missions, as do the other animals at the agency (lampshaded by Vanessa as "a petting zoo... with hats."). It always signifies when he crosses over from mindless domesticated pet to heroic crime-fighter and vice versa. It's a Running Gag that Dr. Doofenshmirtz is incapable of recognizing Agent P without the Nice Hat.
In Hey Arnold!, Arnold makes a big deal of losing his hat which was blown away by the wind, this being because this is the only thing his parents gave him before they disappeared, and recovered by Helga who can now complete her gum sculpture of Arnold. He gets it back at the end.
Dr. Slicer made him take it off simply by telling him to. T.J. does so at once.
The Rocky and Bullwinkle arc "Missouri Mish Mash" centers around Boris Badenov's quest to locate the Kirword Derby, a hat that makes its wearer the smartest person in the world.
The Mad Hatter from The Care Bears Adventure in Wonderland leaves the Bears a series of personality changing hats that leads them to him. Once they do find him he sings them a song about the wonder of hats.
Applejack's stetson in My Little Pony: Friendship Is Magic. So nice, it's the only article of clothing consistently worn by any of the mane characters. Rarity has designed a few of her own, but not for everyday use, and she even incorporates the stetson into Applejack's dress for the Grand Galloping Gala. As for minor characters, Ensemble Darkpony Trixie wouldn't have been nearly so memorable without her pointy hat and ham acting.
Pinkie Pie breaks out a rainbow-colored umbrella hat a couple of times, and later wears a hat shaped like a bowl of chocolate pudding as part of her costume in "Hearth's Warming Eve." Some of the hats from her any costumes include a cake-hat, a basket hat, a working firework-hat and a classy top hat.
The Mysterious Mare Do Well sports a Darkwing-style purple fedora, and Spike gets a white one from Cheerilee for his birthday.
Daring Do from "Read It and Weep" has a fairly-impressive safari hat. She even uses it to escape a Death Trap.
During the Lock and Load Montage in Dragonshy Rarity is first seen with a rather standard steel pot helmet. She then pauses and switches it out for a camouflage pattern sun hat.
During the Hearth's Warming Eve pageant, all six wear headgear that are very telling about their characters. Princess Platinum wears a glamorous crown, while Clover the Clever wears a humble sackcloth hood. Smart Cookie has a sensible pappy hat while the excentric Chancellor Puddinghead wears a bowl of pudding. Commander Hurricane and Private Pansy both wear Greek helmets.
In the Crystal Empire episode, Rainbow Dash and Fluttershy end up jousting during the faire, with even fancier versions of those helmets that use their own manes for the crests.
The Looney Tunes cartoon "Bugs Bonnets" explores the psychological theory that people's personalities can be affected by the way they dress, by littering a forest where Elmer Fudd is hunting Bugs Bunny with various hats. As Bugs and Elmer don each hat, their personalities change accordingly.