Video game example, kind of: The entire fourth installment of the original seven-part (six-part?) Leisure Suit Larry series was never made, largely because lead designer Al Lowe couldn't figure out how to logically continue the series from the third game on and chose to skip straight to the fifth one. Its nonexistence is a major plot point in the fifth game and it pops up in other series by the same company, never playable.
Another explanation is that Larry 4 was originally going to be a massively multiplayer online adventure game (in the early nineties!), but development never got off the ground as modem technology was still much too primitive at the time, so in the end the small minigames that were used to beta-test the project's online capabilities were packaged together and sold as The Sierra Network.
Leisure Suit Larry 4 turns up as a gag/plot point in Space Quest 4. Vohaul smuggled his consciousness onto a disk of Leisure Suit Larry 4, and the Xenonian scientists are so eager to play it that they load it into the planet-controlling supercomputer. When you're in Vohaul's lair later in the game, one of the programs on his computer is "LSL4."
Legend has it that Al Lowe had intended to end the series with 3 and thus once said that "there won't be a LSL4". Well... there isn't.
Here's an interesting example: the sequel to the original Star Fox, Star Fox 2, was never released, even though development on the Japanese version was already completed. The plot would have continued the story from the previous game, and would have introduced Star Wolf as major antagonists. The game was canceled most likely due to the pending release of the Nintendo 64. Shortly after the game's termination, Star Fox 64 began development, and rebooted the storyline from scratch. Eventually the ROM was leaked to the internet, and an English Fan Translation was released.
Many computer games, after their initial publishing run, suffer from a problem somewhat unique to the medium. As Science Marches On, it can be quite rewarding to produce a Video Game Remake or Updated Re-release especially designed for newer computers, except that the source code and other assets of many commercial games are rarely held onto. For example, when the xu4 and Exult projects wanted to make source ports of Ultima IV and VII, Origin admitted that it had lost everything. And when Fallout Tactics was under development just a few years after the previous Fallout game had been released, it turned out that virtually all of the original game's 3D assets had been lost, and nearly all of it ended up being remodeled.
Speaking of Fallout, there's the original sequel to Fallout 2 made by Black Isle, code-named "Van Buren", which was about 85% done when Black Isle's parent company Interplay went bankrupt and the game was never seen again. Fallout 3 was eventually made five years afterwards by Bethesda, yet had nothing to do with Van Buren.
Fallout: New Vegas, however, does reference several concepts that would have been part of Van Buren, specifically Caesar's Legion, the Van Grafs and Hoover Dam. It's no coincidence that the development team for New Vegas was comprised of many former members of Black Isle.
Ultima X: Odyssey: It was canceled just four months after EA shut down Origin.
Many games that don't make it overseas are this to the foreign fans of a series who are cursed with hearing people who actually did get it talk about it, but will never play it themselves. If they're lucky, it's an old game that will get a Fan Translation. If not, they're screwed.
The excessively violent and knowingly offensiveThrill Kill was pulled from distribution before it could offend, likely to avoid fears of a moral outcry, and because AO-rated games are not allowed on consoles. The game developers were rightfully annoyed by this; leaking a beta version of the game before releasing another fighting game, Wu-Tang: Shaolin Style using the same game mechanics, albeit marginally toned-down (i.e., LESS bloody and gory).
Several Amiga magazines were sent review copies of Putty Squad, and even the hardliners at Amiga Power graded it 91%—but the Amiga port never publicly surfaced beyond a coverdisk demo. Only an SNES version was published.
The fourth game in Atari's Swordquest series, Airworld, was never developed, probably due to The Great Video Game Crash of 1983. One of Parker Brothers' Return of the Jedi games also never made it past the concept art stage (the other unreleased game, Ewok Adventure, was discovered as a prototype).
Similar to the Leisure Suit Larry example above, there was an installment of Sam & Max: Freelance Police made called Sam & Max: Freelance Police!!. However, LucasArts cancelled it and it wouldn't be until another two years before Telltale Games would make a Sam & Max game. Like LSL above, the game is referenced in the Telltale Games series as a "particularly gruesome case".
The gruesomeness (and bitterness) around the LucasArts sequel is that the game was finished and already rated by the ESRB, before being caught up in the studio's decision to leave the adventure game business entirely.
The reason why many Sega Saturn classics like Panzer Dragoon Saga and Shining Force III have never been re-released is because Sega lost the original programming code for the games. Same for their System-16 (and then some) arcade games.
Speaking of which, a 1990 Tokyo Toy Show tech demo of the original Sonic the Hedgehog (which was the very first glimpse of the game and also the first time the game could be played by the public) can also considered as this due to a similar situation (the original ROM for the tech demo was lost internally at Sega).
Yet another "lost video game": Despite what many fans believe, the Tiny Toon Adventures video game Defenders of the Universe never got past development stage. Dialogue and graphics were already produced at that time but Treasure simply terminated the project because publisher Conspiracy continuously held off the release date from 2001 all the way up to the spring of 2002, had it been finished. According to rumors, Conspiracy had major financial troubles that led them to pushing the release date numerous times, as well as terminating many of their other planned products. The company told Treasure that "business complications" was the reason they had to wait. It was not until eight years later when an image of a prototype version was shown, and still it looked incomplete (even though the ESRB already reviewed the game at the time of termination, possibly citing that the game was almost complete). Another project, Scary Dreams, was released the same year, but only in Europe (North America did not acknowledge that game's existence until three years later).
This happens constantly with embedded online games (mostly Flash nowadays, but some older ones used Shockwave)
Anything that was on Bonus.com in the late '90s/early 2000s, since the site is now defunct and most of the media on it (mostly games but some stories too) were endemic to it.
Millsberry was an advertisement game for General Mills. It ran for 6 years but shut down in 2010.
The Eyewitness series of educational video games has one of these, if it ever was made. There is an Eyewitness Virtual Reality Shark game referenced to in the others, but no physical copies exist. Not even torrents. It's likely that this one game never was made.
There's actually quite a lot of Super Mario Worldrom hacks that fall into this. Some examples include anything from before the time SMW Central was 'hacked' and wiped clean six or so years ago, any resources use in the Japanese hacks Ore World 2 and The Mario (since the authors websites have vanished along with their asm and code), anything from the first VIP 5 uploader (taken down because people used it for things other than VIP 5 submissions), anything from the original Japanese hack hosting/submission site (which vanished without a trace a few years back) and Super Mario World Freedomn since the author's website has been taken down.
Many user-uploaded cities and components such as buildings and maps of past SimCity games like 2000 and 3000 (the first with an Internet component) have been lost as fan sites compiling those city files for others to play have shut down, bought by larger media companies that didn't care about those archives, or corrupted during site upgrades.
This happens to most MMO's once they shut down.
The Sims Online has been lost but there have been attempts to restore it. The original attempt failed due to EA sending a cease-and-desist letter to the developers but there are others trying with different engines.
Mire Mare, the fifth Sabre Man game, was never made, despite being mentioned by name in the ending of Underwurlde.
Metal Gear Solid Mobile, an award-winning Interquel set between Metal Gear Solid 1 and 2 with a whole new plot and game mechanics, was released just before touch-screen phones became the new thing, and thus was immediately rendered incompatible with everything. Since it was only available for digital download from companies that have now shut down and since phones of that era are impossible to emulate for various reasons, obtaining and playing it is almost impossible, even with piracy - only the NGage version is available on illegal channels and it requires a cracked NGage to play (a discontinued and highly unpopular piece of hardware that goes for hundreds even second hand). There are a few hacker groups working on it, but it's not likely to happen. It doesn't help that it was only available in Japan and to people using Verizon phones in America - so many people in Europe thoroughly missed out.