Hat of Power

Some hats serve more of a purpose than just looking nice. Some even go beyond the mundane purpose of protecting the wearer's head. These Hats of Power grant some superpower or other special ability to whatever lucky chump happens to put them on.

Sometimes, this serves as a more vulnerable version of Clothes Make the Superman (or at least My Suit Is Also Super), since a super fedora is more likely to get blown off by a gust of wind than a super suit is.

Hat of Flight is a subtrope. Compare Weaponized Headgear and Goggles Do Something Unusual.

Anime & Manga

 * Kirby gains a Nice Hat whenever he gets an ability. Some of them are the source of his attacks, generally from the Elemental Powers.

Comicbooks

 * The Marvel Universe has the Serpent Crown, an artifact linked to an Eldritch Abomination that gives wearers various powers. It's an Expy of the Conan artifact (see Literature, below).
 * And let's not forget the Mad Hatter from the DCU. As the name implies, he is a psychotic supervillain with a range of lethal headware. His "normal" hat (if you can call it that) just lets him control people's minds; hats for special occasions include exploding hats, gas-emitting hats, hats that let you fly, and hats with hilarious pop-out guns.

Film - Animated

 * Fantasia, in "The Sorcerer's Apprentice" short, the sorceror's wizard hat gave Mickey magic powers. Or maybe it amplified his own meager powers.

Film - Live Action

 * In Hellboy II the Golden Army, an unnamed golden crown allows its wearer to command the unstoppable Golden Army.
 * The hats worn by members of The Adjustment Bureau are what allow them to use their Portal Network.

Literature

 * In the Nibelungenlied, the Tarnkappe grants the wearer invisibility. Fun thing: It was originally not a hat (cap), but an cloak (cape). Due to changes of language, with kappe shifting its meaning from 'cloak' to 'hat', it became interpreted as a hat.
 * In modern German, the name has become the word for all kinds of stealth technology.
 * In Der Ring Des Nibelungen, the Tarnhelm grants the wearer invisibility, shape-shifting, and teleportation.
 * The Conan the Barbarian novel Conan the Buccaneer features the Cobra Crown, which gives magic powers to the wearer.
 * Discworld: Sourcery: The Archchancellor's Hat has the memories of all the Archchancellors to have worn it and can confer that power/expertise on any wearer it deems suitable.
 * In Robert Westall's Urn Burial, one of the two helmets contained in the burial cairn of Prepoc allows the wearer to gain the martial prowess of the Fefetheils war-leader; letting even a mere human move with the same catlike speed and grace and use the knowledge and tactics of long-dead hunter and warrior.

Music

 * In My Hat by Anthony and Those Other Guys, his hat makes him look cooler, makes him look cooler, cooler than he actually is... and it gets him

Folklore & Mythology

 * Germanic folklore had a helmet that grants the wearer invisibility.
 * Russian folklore had an invisibility cap, usually activated by turning it backwards and otherwise looking perfectly normal.

Tabletop Games

 * Dungeons and Dragons/Pathfinder has many of these:
 * Caps
 * Healing Cap of Veluna: Priest/Cleric healing spells heal double normal number of Hit Points.
 * Nightcap of Vision: Can see in the dark.
 * Pileus: Gives wearer several powers allowing freeing of others from bondage.
 * Crowns:
 * Circlet of Persuasion—raises the wearer's charisma
 * Crown of Blindness—causes the wearer to go blind
 * Hats:
 * Hat of Difference: Can become another character class and gain Experience Points
 * Hat of Disguise -- Exactly What It Says on the Tin
 * Hat of Hatreds—causes the wearer to take on the appearance of someone those around them hate. In addition, the wearer appears to be in a vulnerable condition.
 * Hat of Holding—Allows to pull out a rabbit, two long swords, a spare set of clothes... or whatever adventurers think they may need in the middle of nothing.
 * Headbands:
 * Headband of Alluring Charisma—raises the wearer's charisma
 * Headband of Inspired Wisdom—raises the wearer's perception and common sense
 * Headband of Vast Intelligence—raises the wearer's intelligence (although not as much as the name might suggest)
 * Headband of Mental Prowess—functions in the same way as any two of the above three items
 * Headband of Mental Superiority—raises all three mental stats (Charisma, Wisdom, Intelligence)
 * Helms:
 * Helm of Comprehend Languages and Read Magic—another Exactly What It Says on the Tin
 * Helm of Telepathy—and yet another Exactly What It Says on the Tin
 * Helm of Teleportation -- Exactly What It Says on the Tin (the writers went for descriptive rather than creative names most of the time)
 * Helm of Underwater Action—allows the wearer to see clearly and breathe underwater
 * Helm of Brilliance: Grants many light and fire based spell abilities
 * Helm of Darkness: Can cast darkness, immune to many attack forms
 * Harrowhelm: Grants psionic abilities
 * Skull of Death: Gives several death-based abilities
 * The crown of Nagash from Warhammer Fantasy Battle is a potent artifact, turning the wearer into a necromancer and granting him increased intelligence and magic power at the cost of "hearing voices"—as the crown has personality of its own. It's implied that the crown used to be ordinary, and gained its powers from spending several centuries on the head of Nagash, the great necromancer.

Toys

 * In LEGO's Time Cruisers line, hats are used to power the good guys' Time Machine.

Videogames

 * In the Wario Land series, hats served as Mutually Exclusive Powerups. In the first game, the jet hat allows Wario to fly, the dragon hat allows Wario to breathe fire, and the bull hat allows Wario to Ground Pound while also strengthening his normal charge attack.
 * In Cave Story, the Demon Crown is an Artifact of Doom which grants its wearer magic powers, as well as complete control over a Quirky Miniboss Squad and the frenzied Mimigas. At least one war was fought over control of this Crown.
 * In Kid Chameleon, various helmet/mask powerups enable the protagonist to transform into different forms with different powers.
 * Clonk: In the Defense of the Ancients-like scenario "Keepers", the Hunting Hat boosts your agility.
 * In Last Scenario, Helio wears a speed-increasing hair ribbon, and Flynn has a beret protecting against some detrimental effects. Also, there are items like the Arch-Angel's Halo, which immunizes against all negative status effects and gives huge defence boosts, the Spring Hat, massively increasing HP, and the Crystalline Crown (automatically bestowing P-Shield).
 * Bug!! has the Zap Cap, which allows the titular character to shock enemies in front of him.

Western Animation

 * In "What's Opera, Doc?", Siegfried Fudd had a "spear and magic helmet", the latter of which apparently gave him power to summon lightning and storms.
 * A famous Rocky and Bullwinkle serial featured the Kerwood Derby, a hat that vastly amplified the wearer's intelligence. It's last known wearer was Albert Einstein.
 * Mighty Max had a kid whose baseball cap made him the Capbearer, and apparently the guardian of reality or something.
 * Frosty the Snowman was apparantly brought to life by a magic hat.
 * An episode of Doug had the eponymous character find a hat that gave him amazing luck, which he became so attached too he would refuse to take it off even when getting a haircut. By the end of the episode it flies off to places unknown and everything returns to the Status Quo (band).
 * On The Amazing World of Gumball, the family fights over a Tin Foil Hat that gives the wearer incredibly good luck. Anais takes it to the dump to destroy it, leading to a Lord of the Rings parody with Gumball as Gollum.
 * Willoughby's Magic Hat is an odd 1940s cartoon from Columbia studios - it tells how Samson's hair was woven into a knit cap that gave the wearer super strength. Over the millenia it was a deciding factor in many historic events, and gets purchased by a little schnook of a guy who then faces off against a Frankenstein-like robot menacing a damsel.