As You Know, the Earth is round, and it makes a complete rotation every 24 hours. note Actually 23 hours, 56 minutes, 4.06 seconds — The 24 hours (approximately) is the time between moments when the sun is directly overhead at some point on a given longitude, and since the Earth is revolving around the sun as it rotates, this requires a little more than one rotation. Back when they were formalizing time zones, they had to decide at which point the official transition between one day and the next happened.
This was Serious Business. Wars have been fought over it. For early travelers, the international date line was an almost mystical zone in which a small-scale form of Time Travel was possible. For murder mysteries, an alibi can be made or broken by such a date line.
Crossing this in a ship is grounds for, if you're in the Royal Navy or the United States Navy, being "dowsed" in batter, "shaved", made to drink a mixture that includes chilli sauce and dunked in water.
Historically, the line has found itself moving as politics changed. Alaska, for one, used to be on the same 'day' as Russia ... up until it was bought by the United States, of course. Kiribati was a nation on the west side of the line when it gained independence, until it gained some land on the east. Eventually they just declared the whole thing on the west side (and touted it when 01 Jan 2000 was coming up). Most recently, Samoa and Tokelau both switched from being on the east side to the west side, completely skipping over 30th December 2011. Future revisions may or may not happen.
Note that the date line is mainly an abstract idea. The real 'line' that separates one day from another is when midnight swings by your time zone; thus, when it's 0:00 in Chicago, the date line is really there. And everywhere else that observes UTC -6 (during 'Standard Time') or -5 (during Daylight Savings Time). This tends to draw big celebrations on New Year's Day and any big media release.
It absolutely does not refer toa phone number you call to set up dates with foreigners.
Anime and Manga
The Molmol Kingdom from Love Hina is stated to be placed exactly on the International Date Line. This, of course, becomes a plot point when Keitaro has to return to the Hinata Inn before a certain date.
Subject of a snarky comment in Gremlins 2, when some characters are questioning the vagueness of the "don't let the mogwai eat after midnight" rule.
There's a Donald Duck story by Don Rosa where Scrooge and Flintheart Glomgold try to claim ownership to a newly formed island that's located directly on the International Date Line. The fact that one half of the island has a different weekday than the other becomes a plot point when it comes to determining who claimed it first. It was actually Scrooge's guide, who did it without knowing it.
Around the World in Eighty Days - The protagonists think they have lost the bet, but it turns out they were right on time since they had forgotten to account for crossing the international date line.
And done again in The Three Stooges Around the World in a Daze. Except it's Fogg's decendent, as it's set in the same time (and with the less than bright idea of having the Stooges as wait staff). And this Fogg makes the same error.
The Island of the Day Before by Umberto Eco takes place on the international date line, or at least its characters believe that it does—since they're marooned on a ship in an era before The Longitude Problem was definitively solved, it's tough to know for sure. The characters spend a great deal of time discussing it, often in excessively confused ways (e.g., the Jesuit priest declares that all the extra water required for Noah's flood to cover the land came over the date line from yesterday).
The Edgar Allan Poe short story "Three Sundays In A Week": The protagonist's guardian says he can get married when there are three Sundays in a week, and by inviting over two sailors who have just circumnavigated in opposite directions, he manages to meet the condition.
Arthur C. Clarke's short story "Trouble With Time" is set in a city that was built on the international date line of the planet Mars for some reason. A man tried to rob a priceless artifact from a museum and was caught by the staff when they opened up for the morning. He thought it was Sunday morning (When the museum would be closed) because that's what day it was in the part of the city where his hotel was located, but in the part of the city where the museum was, it was Saturday morning. Avoiding confusing situations like this is the reason why the international date line of Earth was placed in the middle of the Pacific Ocean and zig-zags around to not touch any land masses.
Putting the problem in the middle of the ocean obviously isn't an option on Mars, but it would be even easier to just have the date line run between domed cities and not through the middle of one of them.
Live Action Television
It was mentioned in Michael Palin's first Travelogue Show, Around the World in 80 Days. Like in the Navy Initiation ceremony mentioned above, Michael participated in a rather surreal initiation ceremony on the cargo ship he crossed the dateline on
Discussed in an episode of Power Rangers S.P.D.. Bridge, the Green Ranger, doesn't know exactly what day his birthday is because he was born on an airplane as it was going over said date line.
One episode of Benson (from when the title character was lieutenant governor) had him presiding over a conference of Pacific Island heads of state when two of them (ex-lovers) got into a shouting match. While trying to piece together what happened, it's revealed that Kraus was responsible for the leaders from one side of the International Date Line and Clayton was responsible for the other. Clayton sent Kraus a memo to remove one of the two from the invitations, but she ignored it. It was later revealed that they were to be married, but neither showed up at the church at the same time as the other. It turned out that due to both countries being on opposite sides of the Date Line, one was at the church a day early while the other was there a day late.
One Reader's Digest had a story in "Humor In Uniform" where a naval officer committed a serious offense, got demoted, and lost his pay. However, he was not terribly bothered because his birthday was coming up. Right up until he went to bed the night before his birthday, he smugly expected the crew's obligation to celebrate his birthday. The next morning, he woke up and discovered that the ship had crossed the International Date Line during the night and it was now the day after his birthday.
In a Dilbert comic, the Pointy-Haired Boss asked for questions, saying that "there are no stupid questions". He changed his mind when someone asked "If you crossed the International Date Line on your birthday, would you still get presents?"
Real life: Line Aquavit is a Norwegian specialty in which aquavit is matured in sherry casks stored aboard ships that run from Norway to Australia and back, crossing the International Date Line in the process. The combination of the ship's motion and the trip across the Line supposedly give the aquavit a unique flavor.
While the specifics of its effect on the aquavit are debatable, the tradition of aging wine and spirits in barrels on a long ship journey is at least 400 years old, dating back to when fortified wine would be hauled on Dutch East India Company ships from Madeira to Indonesia before going back to mainland Europe, giving us what we know as Madeira wine.
The log of an American PBY bomber that crossed the Date Line twice during the Battle of Midway records that it took off on June 3, attacked the Japanese on June 5, and landed back at its base on June 4.
If you manage to cross the International Date Line when it's locally midnight, you can either experience a full calendar day twice in a row or skip it entirely, depending on whether you're flying east or west.
So,yes, the Navy can take away your birthday, or Christmas.
A F-22 squadron experienced a major software crash when they crossed the date line, causing most systems to freeze. Fortunately they were able to make it back to base by following their refueling tanker.