Put to use in America 3000 with Gruss, who finds a shiny black top hat as a boy and wears it through the Time Skip into his adulthood, and then for nearly all the rest of the movie. Since the actor playing the younger version of Gruss bears only a passing resemblance to the actor playing the older version, this helps viewers overlook the differences and realize he's the same boy they saw earlier.
Pirates of the Caribbean: Captain Jack Sparrow really likes his leather tricorn. To the point that, when Jack tells the crew to leave his fallen-overboard hat behind (near the beginning of Dead Man's Chest) they know something is seriously amiss. Jack just learned that Davy Jones has sent his pet kraken on a seek-out-and-destroy mission, and Jack's the target.
In Curse Of The Black Pearl, Jack suggests an alliance with Barbossa. Offering to buy him a really big hat seals the deal.
Barbossa himself has a really nice hat. It never once leaves his head in the first three movies, and in the fourth, it symbolizes his return to piracy from privateering.
Geoffrey Rush, who plays Barbossa, does not take it well when his hat keeps getting blown off in the Hilarious Outtakes of the third movie. YE BLEW OFF MY HAT, YE BLEEP!
At the end of CotBP, Will acquires a hat with a big swashbuckling feather, lampshaded by Jack in a possible Trope Namer as he bids adieu to his captors. "And Will... Nice Hat."
Even the cowboys in non-western films like Toy Story. Woody spends an entire scene of the second movie searching for his hat and in the third, Lotso shows it to the other toys to convince them that Woody had died trying to escape Sunnyside.
Dick Tracy had his yellow fedora that matched his trench coat. The novelization of the film said he actually had dozens of them, as they tended to be ruined often in field work, and whenever he had to replace one, he saved the ruined one for a friend who collected them.
In one scene in Indiana Jones and the Last Crusade, he thinks he's lost it and he has a moment of silence for it. The same film has a flashback in the beginning that explains where he got it in the first place (along with many other traits he is known for).
There is a debunked urban legend that the hat was stapled to Harrison Ford's head. (Started, presumably, by an outtake in which Ford jokingly put the hat on his head and then applied a staplegun (empty). He did have to use adhesive tape, though.
The reason the hat never comes off is that the director simply didn't want to have to deal with the nearly-inevitable continuity errors which would have come along with losing the hat. Thus, the Improbably Sticking Hat.
We haven't mentioned that Bond has some nice hats too. Some early films show him throwing it into Moneypenny's office and it landing on the hat-stand. One can only imagine how many takes they must have done to get that shot.
The fedoras Jake and Elwood wore in The Blues Brothers. Notable in that Jake never removed his during the course of the film, and Elwood doffed his only twice.
In The Apartment, the protagonist starts wearing a neat little bowler when he gets a promotion.
"Givin' me the high hat!" said repeatedly by one of the few characters not to wear a hat.
The Spirit is deeply attached to his fedora (and the rest of his outfit) and is caught multiple times ensuring it doesn't get away and recapturing it after fights. The Octopus doesn't have a consistent hat but in his first appearance he dons a very nice hat.
Ryan Evans from High School Musical is known for his collection of fabulous hats- mainly fedoras, but other types of hats have been seen. Due to his parents' immense wealth, he has enough hats to never repeat throughout the entire series. They are seen as his trademark- in the entire series, there are only two scenes in which he is seen without a hat.
Jef Costello, the hitman from Jean-Pierre Melville's crime film Le Samourai, never leaves his apartment unless his fedora is perfectly positioned atop his head. This is less OCD than extreme care about his appearance due to his code of honor.
The Shoveller in Mystery Men sports a miner's helmet. When he gets his costume upgrade, the light on the miner's helmet goes from ordinary-blah white to ooh-and-aah blue.
Ramirez' musketeer-style hat with the peacock feather sweep in Highlander. The Kurgan had a very impressive hat as well, made of a skull and fur.
John Shooter's wide-rimmed black bowler in Secret Window. Doesn't have any special powers, but it is important to the plot.
In Cannibal The Musical, one of the bullying trappers wears a hat made out of a skunk. Whenever he tries to put down the main characters, Matt Stone's character always retorts, "Nice hat!", causing the trapper to look up at it self-consciously.
Van Helsing in Van Helsing - your average 17th-Century vampire hunting hat. See also Real Life examples.
The Mad Hatter in the 2009 Alice in Wonderland naturally has a very nice hat that seems to exist solely to cause cosplayers agony when it's not being used as a form of transportation.
Suffice to say that if he takes off the hat, the odds are good that he's about to do something incredibly risky or more crazy than usual (sacrificing himself to the Red Knights so that Alice can escape, letting Chessur take his place at the execution while he sneaks around behind the Red Queen, and dueling the Knave, to name a few).
Cougar in The Losers has a nice hat he's particularly attached to. It's commented on late in the movie and when a mook tries to take it he dodges out of the way. It appears that even with a gun to his head he's not about to give in.
Mook: You know, I like that hat. That's a great hat. [beat] I really don't care if there's a hole in it. What are you smiling at?
In Dirty Dancing there is a dancer with a Nice Hat. You see him briefly during the dance scene where Baby is carrying a watermelon.
Lawrence of Arabia's turban. At one point, General Allenby is fascinated enough by it to consider trying it on, but then relents, saying it looks better on Lawrence.
Matsu's preferred Roaring Rampage of Revenge garb in the Female Prisoner Scorpion series includes a large-brimmed, dome-crowned black sunhat with a floppy brim. As well as being a decent disguise, it also looks decidedly feminine without being inherently sexy, and the floppy brim frequently obscures one of her eyes, perpetuating the visual theme of Youkai references. The floppy brim disappears in later films, replaced by a flat, rigid brim and crown.