The Hard Hat

One good way to protect your hat (and, in turn, your head) is filling it with something dense. Or perhaps you've got a steel plate in your skull from a long-ago injury, that happens to be just what's needed to deflect a bullet or psychic attack.

This trope contains marked spoilers due to the Unspoken Plan Guarantee.

Examples of The Hard Hat include:

Anime and Manga

Shishio Makoto from Rurouni Kenshin wears a headband lined with steel - the only piece of armor he wears. The reasoning lies in the events of his original 'fall', when he caught a bullet to the forehead, paralyzing him for a while, and giving his enemies time to burn him. He wears the headband to ensure that it never happens again, and it does indeed prove remarkably effective...
Gauron of Full Metal Panic! is revealed to have installed a titanium plate in his forehead due to an earlier injury, and hence is the reason he survived Sousuke's bullet to the head and lives to terrorize poor Sousuke some more.

Comic Books

In one Batman comic, the Caped Crusader is saved from a bullet to the back of the head at point blank range by a magnesium crash helmet (essentially a skullcap) he was wearing under his cowl.
In the 2002 He Man and The Masters of The Universe cartoon it is shown that under his helmet Ram Man appears to have a metal plate grafted to the OUTSIDE of his head. This would certainly come in handy considering his role is to be a human battering ram. It isn't stated if this is because of an old injury but seems plausible considering his teammates Mekaneck and Fisto got their respective metal parts following battle injuries.
During Walter Simonson's run on The Mighty Thor, there was a story arc where Thor fights The Fair Folk with the assistance of an army veteran who turns out to have partial immunity to their glamor because of the steel plate in his head.
Beachhead from G.I. Joe is said to have a metal plate in his head during a crossover with Transformers. In order to sneak through the Decepticon base the Joes cannot have any metal on or in them. Beachhead is unable to go because of his plate.
Played for laughs in a Cattivik story where the person he just hammered on the head happens to have a 10 cm thick steel plate under his hat.
The truck driving super hero US 1 (Or US Ace in latter incarnations) uses this to his advantage in a truckstop fight in the second issue.

Film

The A-Team: in the movie, Lynch tries to shoot Morrison (who's wearing a hood). Instead it's Murdock, and the hood is actually filled with melted ceramic plates.
Faster. Driver has a steel plate which he got after being shot in the head by the men he's now hunting down in his Roaring Rampage of Revenge. At the end of the movie it saves his life after Cop shoots him in the back of the head.
Scanner Cop. The Big Bad initially resists the protagonist's psychic attack because of his steel plate, though it peels away the hair on his head. The cop then concentrates really hard and gets the desired result.
Kick-Ass. After his disastrous first attempt at being a superhero the protagonist ends up with a lot of metal in his body, making it a little difficult to knock him out.
In the old B-Movie They Came From Beyond Space, a character's metal plate prevents him from being psychically controlled by the aliens like all his colleagues.
Bulletproof has Jack Carter, who is shot in the head (accidentally) by his friend Archie. He uses the steel plate on Archie when he's pissed. Later he uses it as a surprise weapon against bad guys.

Literature

In Witches Abroad, Nanny Ogg has a farmhouse land on her head, but is protected by her extremely sturdy hat. Hats that stop farmhouses becomes a running joke, reappearing in later books.
The Tommyknockers by Stephen King. Gardener and Ev Hillman are immune to the Body Horror effects of the spaceship, because they have metal plates in their heads (Gardener because of a skiing accident, Ev because of a war wound). Anne (Bobbi's sister) is apparently helped a bit by her extensive metal dental work, but not quite as much as the two with skull plates.
The Supernaturalist: Cosmo Hill gets a piece of tank armor grafted to his skull from improvised surgery. Allows him to headbutt his way through bulletproof glass.

Live-Action TV

In The Avengers, Steed's trademark bowler hat was lined with steel.
In the pilot episode of the original Knight Rider, undercover detective Michael Long is shot in the face, but survives thanks to the steel plate he got after brain surgery for a Vietnam War injury. The bullet severely damages his face, but thanks to Magic Plastic Surgery he can now return as Michael Knight.
Drop the Dead Donkey: Jerry the Camera has a "suicide by jumping" land on his head (thanks to Damien demanding he get right in underneath for the shot), however he is saved from injury due to the steel plate he has in his head from Damien's piece on why plastic bullets are safe.

Web Comics

A throwaway gag in a filler strip in Knights of the Dinner Table has Newt claiming his character is crouching real low and taking cover behind his 'kevlar watch cap'.

Western Animation

The Dick Tracy animated series from the '50s/'60s had "Joe Jitsu" with a hat with a German WWI Helmet underneath it that protected him from a bonk on the head
SpongeBob SquarePants: "A good fry cook always keeps a piece of lead under his hat." In this case, it's to protect the hat from being stomped on.
In the Looney Tunes short "Rabbit's Kin", Pete Puma comes prepared for Bugs Bunny's Hyperspace Mallet with an Acme Stovetop Lid under his hat. The Crazy Prepared Bugs then produces an Acme Stovetop Lid Remover...

Real Life

Truth in Television; Bowler hats were conceived as alternatives to top hats that were better able to protect the wearer's head. A properly made one is quite rigid. The same goes for modern police hats (they look like soft caps, but they're quite hard).
Hard hats, of course.