Once Upon a Time, when bladders were smaller, attention spans were shorter, and people actually went to the theatre to see films instead of illegally streaming them off the Internet, there was a thing called an intermission. This was a time when people got out of their seats and walked around in the lobby talking with their fellow patrons of the arts and using the facilities. This broke up the pacing of a film and changed a monolith into something considered in smaller parts. During the intermissions themselves, it was common to show cartoons with catchy jingles enticing the audience to head to the lobby and buy themselves some refreshments.
These days, intermissions are far less common, but that hasn't stopped them from popping up in all sorts of media, including a few where they don't even seem to make sense, such as webcomics. Films are still the most common source outside of live theatre though, especially Epic Movies. Bonus points if the intermission is included in the home video version. Some cinemas (especially smaller ones) will also insert intermissions into the films being shown even when there was no original split.
In Theatre, intermissions are still standard practice. They provide a break to let the stage crew change the set around. Also, theatrical productions tend to be relatively long, and also tend to frown heavily on people leaving and returning during the performance, so intermissions are much more of a biological necessity. (And actors need bathroom breaks, too.) There also an economic benefit, as theatres can make some sales at the bar and/or snack food stands (but the food and drinks have to be consumed outside of the auditorium). In other media, standards tend to be more lax. As almost all theatre productions involve intermissions, don't list one of them here unless it's particularly noteworthy.
Lengthy concert performances by musicians or stand up comedians may also include an intermission, to give the performers a break and to allow for possible changes in the lineup. During the intermission, backup performers may provide light ambient music to entertain people who don't choose to leave their seats, but featured pieces will be reserved for when the show resumes.
This trope exists in sports as well. American football and basketball have halftime. In American baseball, an intermission takes place in the middle of the seventh inning, and is referred to as the "seventh inning stretch". National Hockey League games usually have two intermissions of about 18 minutes each.
If you're looking for the 2003 film, see here.
Gettysburg came with an intermission, at least when it was shown in a theater. But then since it was planned as a four hour, two day TV Mini Series before they decided to show it in theaters...
When the full version of Once Upon a Time in America (which runs 3 hrs 49 min) was shown on The ABC (ABC is Australia's public broadcaster and doesn't have commercial breaks), they included an intermission.
Oddly said intermission (at about 2 hours and 40 minutes in) is also on the DVD, but cut down to a couple seconds.
When Schindler's List was broadcast on television for the first time (at least in the USA). NBC's airing of the movie was commercial-free and without breaks, save for a two-minute interval in the middle with a timer counting down to when the movie would resume.
The film version of Oliver! kept the intermission from the stage play. On the DVD, the Intermission also doubles as a prompt to turn the disc over to continue the film.
The original roadshow version of Fantasia. Later versions re-edited the footage of the orchestra leaving for intermission and then returning for the opening and closing of the film. The DVD version restored the original intermission footage.
Butch Cassidy and the Sundance Kid included a ridiculously long (FIVE MINUTES) montage of still photos which served very little expository purpose. It is not an official intermission, but it is a great time to go to the bathroom.
The film of The Sound of Music had its intermission in a different place than the stage version. The play ended its first act on the Mother Abbess singing "Climb Every Mountain", while the movie relocated the break to follow Maria returning to the Abbey.
How the West Was Won - because the Cinerama system used giant horizontal film reels, the Intemission was essential to facilitate a reel change.
Gandhi has a black-screen intermission in which Indian music plays. Necessary, given its 188-minute running time. When HBO ran the film in the mid-1980s, the network ran its own intermission graphics with a timer counting down to when the film will resume.
Evangelion: Death & Rebirth has a five minute intermission between parts. The sequel is divided into two episodes, and while not having a true intermission, the film's credits play after the first episode.
Kingdom of Heaven The extended version had this for its limited theatrical release, and keeps it on the DVD version as well.
The extended edition DVDs of The Lord of the Rings trilogy have intermissions that also tell the viewer to pop in disc 2 to see the rest of the movie.
The above example was also used in the original DVD release of Pearl Harbor. An "Intermission" title card appears after Roosevelt's "day that will live in infamy" speech. In that case, it told the viewer to put in disc two.
West Side Story had an intermission during its premiere, but later lost it for several decades' worth of theatrical and home video re-releases, since director Robert Wise felt it broke the tension.
Molière wrote a play with a whole other play that goes on during intermission.
This was actually standard practice for a long time, only with other playwrights plays happening in the intervals. A three-act drama could have a short two-act comedy within the intermissions. There are a huge number of short operas that exist to be played in the intermissions of longer operas, both as a chat/bathroom break and as a mood lightener.
There's a scene near the end of the stage musical version of The Producers where one of the characters recaps everything that's happened so far — including the intermission.
There's also a scene where the two main characters walk in and find their office has been completely repainted; they ask their assistant when she had time to do that and she replies "during the intermission".
Vanities: A New Musical had one in its Theatreworks premiere, but it was later dropped. During this, Mary sang about her trip to Europe in the song "Open Up Your Mind".
In keeping with their commitment of showing "movies as they were meant to be seen", Turner Classic Movies often shows movies with the original intermissions.
1970s BBC Radio sketch show The Burkiss Way had a "brief intermission" in each show (always preceded by "Theme from A Summer Place"), generally consisting of sketches that had a separate theme from the rest of the show. On one occasion the Intermission took up about 90% of the episode.
Stand Up Comedy
A tradition at nearly all of Ross Noble's gigs is for audience members to leave bizarre gifts on the stage during the interval. The more interesting ones will usually be incorporated into the show somehow. And given his penchant for going off on many different tangents, and taking quite a long time to make his the point, the subject of the interval/intermission will usually crop up doing his set:
"Please can we have an interval Ross... PISS IS GONNA COME OUT OF OUR EYES!!!"
Those who decided to skip said intermission don't realise they missed a whole bunch of plot-relevant stuff...
Act 6 is made of multiple sub-Acts, each with an intermission in between - to the point that Act 6 Act 4 was a four-minute flash animation surrounded by Act 6 Intermission 3 and Act 6 Intermission 4, both of which are extremely long.
Seen in the Tex Avery cartoon "What's Buzzing, Buzzard", which poked fun of food rationing during World War II. At one point a character imagines a T-bone steak with all the fixings, and there's a five second intermission "for drooling".
Quest For Glory 2 parodies this with an intermission during the off-screen brigand battle. During an extended cutscene, your desert caravan of perhaps twenty is assaulted by hundreds upon hundreds of bandits, and even the narration box comments that things look hopeless. Then, intermission! And when you finally hit the space bar to return to the game, the first thing you see is your hero standing apart a true mountain of dead people, and the caravan reduced to about 7.
Wet has fake intermissions, both as part of its Grindhouse aesthetic and to cover loading times.
Pac-Man was probably the first game to have intermissions (and they were even called that) - short animations every few screens to break up the gameplay. This was continued in several of the game's sequels (Ms. Pac-Man, Jr. Pac-Man, Super Pac-Man, Pac-Mania, etc).