Murlynd's Hat. In the GreyhawkD&D setting, Murlynd of The Company of Seven's leather chapeaux can have near any non-magical object be pulled out of it, and it grants a degree of protection. He also had revolvers and a whip, making him probably the most badass wizard/paladin in existence. But the hat man...the hat.
In the Forgotten Realms setting, Elminster's large wizard's hat is one of his most distinguishing features. (Along with his flowing beard and smoking pipe).
Warhammer Fantasy: The Empire. Every bloody soldier has some sort of outrageous wide-brimmed plumed construction, or a massive plume on a metal helmet. Except for the archers. Grand prize has to go to the triple-feathered hat in the Empire General kit, though (the one on the mounted guy in the picture).
The Chaos Dwarves apparently had hats whose height reflected the wearer's status. The superstructure of their warships also tended to look like giant versions of their hats.
Heinrich Kemmler's model gives him a very distinctive Robe and Wizard Hat - the robe appears to be sewn out of skin, and the hat is a giant pointy thing with at least two skulls on it.
Warhammer also has the Witch Hunters's Hat of Doom. Characters have take a will test against fear just by seeing it.
The Lizardmen Skink Hero riding a Stegadon gets a choice between a skull hat (for a wizard) and a rather badass gold stegadon mask for a fighty hero. And for all your giant mummified frog fashion needs, there's Lord Kroak's deathmask. Of course, since so few Lizardmen wear any clothing at all, they have to make the headgear badass.
The Magic Burner for Burning Wheel covers wizard characters, who as part of the traditional Robe and Wizard Hat can find themselves with the "Impressive Hat" described as follows:
This character's hat is mightily impressive. It can be seen for miles! It's so impressive that people often remember the hat more than the person.
Munchkin has several, such as the Bad Ass Bandanna, the Helm of Peripheral Vision, the Horny Helmet, and the Helm of Courage (which is on backwards). For the grand prize, we have...the Magnificent Hat, complete with what appears to be a Jägermonster looking unusually proud. Does any other game have a hat so nice it reflects curses? Nope.
Many characters in Privateer Press's Warmachine tabletop game have pretty nice hats, but special props go to Protector of Menoth for their multitude of clergy hats and Deneghra for hers. Since the setting is Steam Punk, it's kind of required to have one.
In the party game Werewolf/Mafia, a role with a Nice Hat, Big Hat or White Hat will always be revealed upon elimination, even if roles would normally be hidden. A Black Hat, by contrast, will never be revealed regardless of circumstances.
The fan made game Touhou: Mystical Yokai of Necrophantasia (usually shortened to MYON) is based on the Touhou video game series where every character ever either has a nice hat or a fancy ribbon. NO EXCEPTIONS. This is so prevailing that Hat is actually a stat for characters!
Of course, the monster with the coolest hat in the game is arguably Cosmo Queen. Seriously, just look at it! So much that it's become a tradition in fanfics for someone to comment on it when she appears.
Then there's Amplifier, or as GX Abridged called it, the Snazzy Party Hat. A hat that sharpens psychic powers is pretty dang nice.