The Hidden Hour

The Hidden Hour is a period of time within the average day that is Invisible to Normals; most people don't experience it, nor are they aware it even exists at all. Only a few people, often those with some kind of special power, know about this extra hour; and only they are able to act during it. To these people, when The Hidden Hour occurs, normal clocks stop ticking, Muggles freeze in place (or vanish entirely), and strange things start to happen.

The Hidden Hour frequently occurs When the Clock Strikes Twelve, due to the association between midnight and magic. However, this is not about magic simply being at its strongest around midnight, nor is it about planets whose day-night cycles are naturally longer than 24 Earth hours.

In spite of the name, The Hidden Hour is not necessarily 60 minutes long; it frequently lasts as long as the plot requires, which to those involved may feel like several hours, or possibly even days, before the Hidden Hour ends and normal time resumes.

Anime and Manga

 * There's a short manga called Crossing 25, in which the 25th hour is inhabited only by a handful of people who fight over whether tomorrow will arrive or not. It's... interestingly strange.

Film

 * Dark City has something along these lines, with everybody just falling asleep on the spot at the appropriate time. Fortunately, all cars and trains in the movie seem to have "Sleeping Man Switches" to keep them from plowing into things or each other.

Literature

 * The Midnighters Trilogy has the Blue Time, between midnight and 12:01, though in the last book it starts appearing during the day as well. Also involves monsters which attack the defenseless ordinary people (or would were it not for the efforts of a bunch of teenagers who fight them with superpowers and the number 13).
 * The book Tom's Midnight Garden has Tom able to access the titular garden  when the clock in his aunt's house strikes 13 at midnight.
 * Philip Jose Farmer's Dayworld books have a slightly more science-fictional version of this. To combat overpopulation, just about everyone is in stasis six days out of seven, and there's a half-hour gap between the time one day's population goes into stasis and the time the next day's population comes out.
 * The famous science fiction story Zeepsday by Gordon R. Dickson is about an alien race that shows humanity that there is an eighth day in the week.
 * Clive Barker's Abarat Trilogy deals with a magical archipelago where each hour of the day is represented by an island. There is a 25th island, that remains highly mysterious even after it's visited.
 * The Eleven-Day Empire, from the Doctor Who Expanded Universe, was created from the "missing" days between 3 and 13 September 1752.
 * The entire plot of Stephen King's short story "The Langoliers" from Four Past Midnight. Several people wake up on an airplane mid-flight to find themselves all alone in the world and

Live Action TV

 * In The New Twilight Zone episode "A Matter of Minutes", a couple are caught in a space with no time where the future is being constructed for each minute.
 * This is based on the short story "Yesterday was Monday" by Theodore Sturgeon.
 * The same series also has "Paladin of the Lost Hour", where there's a secret hour contained in a pocket watch and only revealed to one person at a time, but it's a borderline example since the hour never actually occurs (if it did, the world would end).
 * Stargate SG-1 had the main characters effectively experience one of these. They were on a planet where people were linked into a computer system. Every so often, the computer would "pause" everyone. During this time, the team walked around while the population was frozen.

Music

 * "25 O'Clock" by The Dukes of Stratosphear.

Tabletop RPGs

 * Don't Rest Your Head has a hidden hour that occurs twice a day, once at noon and once at midnight.
 * However, this extra hour occurs only in the Night City; no-one in the real world, supernatural or not, experiences it.

Video Games

 * Persona 3 has the Dark Hour, between midnight and 12:01, wherein monstrous Shadows roam free and ordinary people turn into coffins.
 * Terranigma the opening sequence makes reference to the clock having 13 hours, which leads to an important plot point later.