Staring Contest

A Staring Contest is a competition where a number of players (usually two) must lock sights with each other's eyes and stare as for as long as possible. The first player to look away or blink loses.

Mordecai: Hey! No laser pointers! That's not regulation!

Rigby: Street rules, man!

—Regular Show, Peeps

As an optional rule, the players may do anything they want (without touching the other player) to try to get the other player to look away or blink. The stock joke is for one participant to be something that cannot blink.

Compare Staring Down Cthulhu, which is a bit more extreme.

Examples of Staring Contest include:

In Order of the Stick, Xykon forces O-Chul to get in a staring contest... with a basilisk.
- Which O-Chul won. Technically, he never blinked.
The fourth case in Ace Attorney Investigations reveals that Edgeworth once won a glaring contest against his own reflection. Somehow.
Featured in Hi Hi Puffy AmiYumi.
In the Discworld novel Lords and Ladies, Granny Weatherwax is challenged to a staring contest with a twist by up-and-coming witch Diamanda. They won't be staring at each other, but at the sun.
In Courage the Cowardly Dog, Katz and Courage have an epic duel to the death in the form of a staring contest.
In Wapsi Square, Shelly cheated in a staring contest to get out of paying her bar tab.
In Real Life, the easiest (though admittedly underhanded) way to win a staring contest is to blow gently into your opponent's eyes so that they will be forced to blink due to dryness.
Derren Brown once challenged random passersby to a staring contest. Somehow, without saying anything, he would cause the other person to feel very uncomfortable and close their eyes. In one case, a guy actually screamed and grabbed his head, until Derren helped him. This only fuels David Tennant's conclusion that Derren is a witch. See the contest here.
A Garfield strip has the titular character initiate a staring contest against a goldfish. Then Jon informs him that fish don't have eyelids.
In Tales of Monkey Island Chapter 2: The Siege of Spinner Cay, Guybrush places Hardtack and Trenchfoot into a staring contest, into which our hero can distract the pirate duo into looking behind them so he can place the Pyrite Parrot into the treasure chest, in hopes that he can find where they'll bury it along with one of the Summoning Artifacts later.
Aquarium described how, during his time in the Spy School, the narrator was taught that no man can be recruited unless you can win a Staring Contest with him; otherwise, he has the stronger will. Suvorov spent quite a bit of time in the zoo, staring down tigers as practice.
Doctor Who Weeping Angels ability (they can't move but can't be hurt, as they lock themselves out of time, when being looked at) forces you to get into these for your life. If you so much as blink, the Angel is going to Flash Step next to you and kill you before your eyelids have time to open again. They also have a second sneaky trick in that if you look them directly in the eye, they will animate the image of the angel in your retina, which will claw it's way out of your eye and kill you anyway. To be safe, you have to look at them, but NOT in the eye.
SMBC Theater offers us the ultimate Staring Contest, which is quite extreme.
In Judge Dredd, as of 2134, competitive staring is a professional sport in Mega-City one with a relatively small but growing following.
Socrates attempts to have one with a duplicate of Andy in Calvin and Hobbes: The Series. Since the clone doesn't blink, he loses.
Not Always Right had a guy who actually tried to stare down a snake.
Sinfest had a Staring Contest mini-arc. And then Devil challenging Jesus to a staring contest (the Devil, naturally, tries to cheat). And a lil' angel challenges Lil' Evil.
Forgotten Realms novels usually describe mind-to-mind fight like this, and usually the attacking side starts with making it impossible to avert gaze.
Tamers Forever Series apparently had a case when two characters stare into each other's eyes... and stare... until one of them forgets what the original idea was. It's more strange that this doesn't happen more often.