When asked about the Bat-Hat, the artist responsible justified it with "I took a lot of crap from friends about this hat. But I still like the design. Russia is cold, why can't Batman have a warm hat?"
Perhaps not quite the same, but in the newspaper comic Curtis, the title character often gives commentary on the church ladies' more and more extravagant (and silly) hats.
Curtis himself is always seen with an oversized green cap — he even sleeps with it on.
Galactus cares not what lesser mortals think of his hat!
This one is a personal favorite of Superdickery's author, by the way.
In an issue of the Marvel G.I. Joe comic series, Firefly unveils his new outfit. The Joes he's facing are less than impressed. He notes that "you don't get the full effect without the hat" and puts his on (it's more of a helmet, but whatever), and although he's supposed to be a terrorist but is wearing neon green, he does look commensurately more badass.
In the Hitman comic, Tommy Monaghan's best friend is Natt "The Hat" Walls. The hat in question is very nice indeed, and damage to it appears to serve as a Berserk Button for Natt.
There's a particularly interesting use in Excalibur v2 #11, where Magneto comes back home to Xavier after taking Scarlet Witch away from the Avengers. Charles reprimands him about wearing his helmet and Mags responds defensively, only calming down once he's taken the bucket off his head. Of course, this likely had more to do with the ridiculous amount of power he had just used, but the helmet was a good symbol.
He wears it when he feels a particular need to shield his mind from Xavier—which usually means he's up to something nasty.
Speaking of the Scarlet Witch, in her first two dozen or so appearances, Wanda's "hat"/headcover was more like a lampshade with a hole in the front for her face.
The Juggernaut's Helmet which also keeps Charles out of his head. And the skull cap he wears underneath, which is also psy-proof.
In an issue of The Books of Magic, Zatanna is having a conversation about good and evil with the Affably Evil Tala. The latter is wearing a particularly stylish hat. Zatanna finishes her argument about how good is better with "It's the only thing that keeps me from stealing your hat." Not that Zatanna is any slouch◊ in the headgear department herself.
Watchmen: Rorschach wears a fedora. During the movie version, during the fight with Ozymandius, whenever his hat falls off, he won't fight until he's put it back on. This seems to hint that he considers it to be a part of his 'body', as he does his mask.
Alpha Flight villain/hero Smart Alec has a big, bulky helmet that also enhances his intellect and feeds him information at a superhuman rate.
The Mad Hatter is a Batman villain who not only has a hypnotic (literally) chapeau of his own, but who's fascinated with all headwear, especially the nicest one of all— Batman's cowl.
Lots of Batman villains have very nice hats: The Riddler has been known to sport a green bowler hat with a question mark, the Penguin usually wears a massive top hat, and the Joker sometimes accessorizes with a purple gambler hat◊. Niiiice.
Though he only wore it once and it was part of a specific tourist-themed outfit, the Joker's straw-brim hat from when he shot Barbara Gordon is also memorable.
Half the Gauls in Astérix wear nice helmets. The winged headgear worn by Chief Vitalstatistix actually has a chicken fall in love with it.
DC's Doctor Fate has a helmet which is the source of his power; it originally contained the spirit of Nabu that possessed Fate when he wore it. If put on by an enemy, the helmet would drive them insane. Later on, the helmet also fought evil on its own, approximating a body with his gloves and cape. Although Nabu left the helmet to usher in the new Age of Magic, it still has enough magic to impart knowledge to its host and contend with those that might abuse it for their own ends.
Dum Dum Dugan from Sgt. Fury and his Howling Commandos is very attached to his bowler. A major subplot in one of the issues involves the hat getting destroyed and Dugan's attempts to replace it. (His squad-mates get together to buy him a new one. D'awwwww.)
The Sandman: Death of the Endless has a floppy hat collection. She also borrows Emperor Norton's hat (see Real Life below) when she comes to collect him.
Can't forget Dream's trademark Alien-in-a-gas-mask helm (a Shout-Out to the 1950s Sandman series), which he dons whenever he has serious business to take care of.
The Shade normally sports one in Starman, but he occasionally swaps out for a variety of other hats.
In Calamity Jack, the sequel to Rapunzel's Revenge, ActionCowgirl Rapunzel buys a hat in Shyport, the Big City. It's right nice and smart, making Rapunzel look all citified and stylish and suchlike. The acquisition of Nice Hats is also the obsession of their friend Prudence, a pixie, who likely pointed Rapunzel to the city's finest haberdasher for the acquisition of her new chapeau.
The Redeemer from the Necromunda Comic of the same name. His flaming crown also doubles as a weapon, allowing an extra degree of Kill It with Fire when in a pinch.
Enemy Ace Hans von Hammer has very distinctive flying headgear.
Wolverine can usually be seen wearing a cowboy hat when out of costume.
Several characters Jack Kirby designed for the Thor mythos have gigantic, lavish Nice Hats, particularly Loki and Hela. Indeed, Kirby created a great many Nice Hats over his long career, as shown in the ongoing feature from Bully, the Little Stuffed Bull, The 5,000 Hats of Jack Kirby.
Phrygian cap style hats are pretty much standard clothing for The Smurfs. They may vary in appearance depending on the occupation of the Smurf wearing it, but they are rarely seen without it. Since male Smurfs are bald, the hats can be used to smuggle things (like in the Animated Adaptation's Greedy Smurf, who hides a dessert under his hat, or Clumsy, who hides an Explosive Breeder). In the live-action movie, the hats also serve as parachutes to slow the Smurfs' descent as they jump from the Winslows' apartment window in New York City to a nearby taxicab.
Abuse wears a fedora in his "adult" form along with a trenchcoat. Mostly because he's actually ten and so doesn't really have clothes that fit him when she shifts. Damian Wayne doesn't seem to think it's very cool, though.
No one has mentioned the guy Jim Steranko called "The Snapbrim Superhero"...namely, the Spirit.