Brain Freeze

Characters eating cold food or drinks too fast will get a "Brain Freeze". Almost universally a Comedy Trope. Brain Freeze will be treated as the most searing pain imaginable. Expect to see rivers of tears, screams of anguish, and the victim frantically clutching his head in agony.

Truth in Television; you most definitely can give yourself a headache by eating cold food too quickly. This is due to the blood capillaries in your sinuses; cold food causes them to constrict, and then experience extreme rebound dilation as they warm up again. This rebound triggers nearby pain receptors, which the brain interprets as coming from the forehead. You can recreate this effect when you put an ice cube on your forehead (and you don't have a headache, that is).

Now, if you want to prevent it, just lick your soft palate before diving into that milkshake and you should be fine. Eating warm or hot food can also help.

Examples of Brain Freeze include:

Advertising

A McDonald's commercial from two decades ago has a boy telling the audience that one of his lifelong ambitions is to become a scientific genius so that he could cure "that thing that happens to your head when you eat ice cream too fast." (Exactly what this had to do with McDonald's, I can't remember.)
A 1990s 7-Eleven TV spot was perhaps the Trope Namer. It featured a young man ingesting a Slurpee, letting loose a bloodcurdling scream, and then explaining: "Ugh. Brain freeze."

Anime and Manga

In the Cowboy Bebop episode "Mushroom Samba", a one-shot character is eating ice cream when a Chase Scene in progress passes him. He decides to join in, but rather than abandoning his ice cream, he attempts to gobble it up all at once. He does not enjoy the resulting Brain Freeze.
Used by Team Rocket in the Pokémon anime, giving the characters loads of ice cream and then stealing their Pokemon while they were disabled by the freeze.
In Demashita! Powerpuff Girls Z, the girls have a brain freeze after eating some ice cream, which repels the powers of Him that had transformed them temporarily into little girls, as he had a weakness against cold.
In one chapter of Kochikame, Ryotsu bought a shaved ice maker and a big block of ice to make shaved ice bowls to eat which he got addicted and goes far as making sushi with ice rather than rice. His addiction got him severe brain freeze ends the chapter with him laying down with bags of ice over his forehead.
Ururu in Okusama wa Mahou Shoujo gets one from sweeping an iced drink. She does it again once she gets a refill.

Film

Hot Fuzz: Double Subverted after Nick has a Eureka Moment while they're eating Cornettos;

Danny: What's the matter? You got brainfreeze?
Nicholas: No - brainwave! Get us back to the station. Now!
Danny: [tries to swallow his Cornetto whole] ARGH!

In Encino Man, Link experiences one of these after Stoney's lesson on "wheezing the juice". His mouth is still full of Icee as he silently clutches at his head.

Live Action TV

In one Scrubs episode, a patient's wife is approaching Turk and Elliot in the cafeteria. Turk declares the first one to chug their Slushie is off the hook, and proceeds to give himself brain freeze.
On Cheers, Frasier can't get Norm to understand what a stress headache is until he compares it to eating ice-cream too fast.
On Step by Step, Cody gets a brain freeze, so (someone... Dana, possibly) advises him not to (consume his frozen foodstuff) so fast. Cody remarks that he wouldn't get the brain freeze if he stopped. Apparently, this is a desirable condition for him.
The Adventures of Pete and Pete: In "Field of Pete", the brain-freezing power of the Orange Lazarus slushy incapacitates anyone who drinks it. The legendary drink has since spawned a Pete and Pete fanlisting, an improv group, and a band.

Newspaper Comics

Garfield once had the character trying to eat his ice cream cone in one bite, despite Jon warning him not to. We see him writhing in great pain, his bloodshot eyes bugging out like the suffocating Martian colonists in Total Recall.

Stand-Up Comedy

When Steve Geyer was young, the kids called them "Slurpee Tumors".

Toys

in 2004, Milton Bradley had a sweepstakes called "What's Ailing Sam?" where fans could vote on what new ailment to give Sam for the game Operation, and gain a chance to win a $5,000 shopping spree. The choices were "Growling Stomach", "Tennis Elbow", and "Brain Freeze". Brain Freeze won.

Western Animation

In one episode of The Angry Beavers, there was a dare to drink a huge frozen jalapeno milkshake. There was reluctance to take this dare, for fear of a "brain freeze and burn", which is this Brain Freeze combined with Fire-Breathing Diner.
Megas XLR: Kiva gets one after drinking her first Mega Slush. Something similar appears in the opening credits.
Teen Titans: played literally when Beast Boy throws The Brain to be frozen.

Beast Boy: Hey, check it out! [flash-freezes The Brain] Brain freeze!

Taken Up to Eleven during a Manatee Gag in Family Guy, where Peter's head explodes after eating an entire ice cream popsicle in a single bite.
Numbuh One from Codename: Kids Next Door never got a brain freeze. This is a plot point in one episode, as Professor XXXL gets extreme brain freeze and needs Numbuh 1 to test out recipes for the perfect snow cone.
The Weekenders use this as a way to "draw straws"... they all start drinking their Slushees at the same time, and whoever stops first due to brain freeze, loses.
In one episode of Bill and Ted's Excellent Adventures, the lads experience a synchronized brain freeze after meeting their own challenge to drink very large Slurpee analogues in an inadvisedly short period of time. This is portrayed as a harsh guitar riff and Screen Shake as they cry out in brief agony.
Happened to Earthworm Jim at one point - particularly bad, since earthworms have four brains, and they all froze at once.
The Fairly OddParents: Timmy is seen with a brain freeze from eating a "Sloppy Slush" too fast. Cosmo then finishes it in seconds and feels nothing. Later in the episode, Timmy invokes this to defeat the Big Brain.
One episode of The Simpsons had the church hold an ice cream social, complete with a brain freeze clinic. Cut to a severely-affected Nelson getting an oral hot fudge injection.
On Jimmy Two-Shoes, Jimmy gets this by...shoving ice cream onto his head.
In Phineas and Ferb The Movie: Across the 2nd Dimension, feature-length film, one of Perry's special weapons will give the victim an ice cream headache.