1. The Los Angeles Vault
The Los Angeles Vault was the very first vault, and played heavily into the plot of the original Fallout game. It was created by Vault-Tec Industries, and served as a prototype for all their other vaults. It opened 15 years after the Great War that decimated Los Angeles, and its dwellers formed the city of Adytum near its entrance.
Many flocked to the city and the vault below it, including a grotesque monster called the Master, a product of a process called "forced evolution" that transformed him into a hybrid of a vault computer and a man. The Master turned the vault into his lair, and conducted experiments on its dwellers in an attempt to create more creatures like himself. Instead, he ended up creating a race of brutes known as the super mutants, who served as his personal army.
The vault was destroyed during the events of the original Fallout when a nuclear device was set off under the structure by the game's protagonist.
2. Vault 11
Vault 11 was sort of like a large scale Milgrim experiment, and the dwellers within were instructed to sacrifice one inhabitant per year. As long as the sacrifice was made, they lived in comfort, with all the food and amenities they needed. The victim was democratically elected, and would spend a year as the Overseer of the vault before retiring to the sacrificial chamber and being killed by the vault's computer systems.
After several years, the population formed into voting blocs. The most powerful of these blocs, called the Justice Bloc, would blackmail people into doing favors for the group. In one such incident, members of the Justice Bloc coerced a woman named Katherine Stone into performing sexual favors for the group. If she refused, the group threatened to nominate her husband as Overseer and sacrifice.
Katherine complied, but the Justice Bloc nominated her husband regardless. She got her revenge by killing off members of the Justice Bloc one by one until they no longer had a voting majority. For her crimes, the vault dwellers elected her as Overseer, which was actually part of her plan. Her first act as Overseer was to change how the sacrifice was chosen, which would now be decided by a random lottery. The Justice Bloc staged an armed coup to overthrow Katherine Stone, and all but five of the vault dwellers died.
The final five survivors decided to commit suicide together. In doing so, they missed their opportunity to perform the sacrifice. It was then revealed by the computer that the experiment was designed to play a "automated solution response" praising the vault dwellers for being a "a shining example to humanity" in the event that they refused the sacrifice, and the vault was designed to open allowing it residents to come and go as they pleased.
3. Vault 22
Vault 22 was designed to be fully sustainable. The entire population was meant to thrive solely on plants grown within the vault, which was going fine until they all turned into mindless monsters.
One of the plants included in the experiment was an entomopathogenic fungus called Beauveria Mordicana, which was being used as a natural pest control method. Shortly after the vault was sealed, the fungus adapted the ability to infect human hosts. The dwellers of Vault 22 breathed in the spores, which began as an infection in their lungs, but quickly spread to the rest of their bodies and eventually caused total organ failure. Once the host had died, the fungus hijacked the hosts body, turning them into mindless, dangerous spore carriers.
Society within Vault 22 collapsed, and after a few unsuccessful attempts to halt the spread of the fungus and the spore carriers, the remaining survivors abandoned the vault. Vault 22 fell into disrepair, and the plants that were meant to sustain the populated quickly grew to choke the narrow tunnels and passages. Aside from the plants, the only population that remains in the vault is the zombie-like spore carriers.
4. Vault 29
Vault 29's population was meant to made up entirely of children. Rather than a traditional human Overseer, Vault 29 would be managed by a supercomputer, and robot helpers would help raise and educate the young population. When conditions returned to normal, the children would be released and would rebuild society, untarnished by the influence of the destructive generation that came before them.
Obviously, there were some complications, and experiment never reached its conclusion. Instead, the children of Vault 29 eventually escaped and formed the village of Twin Mothers above their former home.
One of the most notable dwellers of Vault 29 was Harold, a mutant who appears in most of the Fallout games, and who would eventually transform into a living tree.
5. Vault 34
Vault 34 was designed with a huge, well-stocked armory, many recreational facilities, and very few living spaces. It wasn't long before the vault became overpopulated, and the dwellers became disgruntled. Expecting the worst, the vault's overseer had a lock installed on the armory that only he could unlock.
The residents of Vault 34 began to riot. A group calling themselves the Boomers gained access to the armory, and used the weapons to blast open the entrance to the vault and escape. (They would go on to take over Nellis Air Force Base and create their own tribe.)
The Overseer of Vault 34 regained control, and life went back to normal, except that the door of the vault was damaged and would never fully close. Guards were posted at the door at all times to keep the population in and bandits and mutants out. Other sections of the vault went neglected, and before long, the nuclear reactor began to leak radiation.
Almost the entire population of the vault would eventually succumb to radiation sickness, and most of them transformed into glowing, well-armed ghouls and mutants.
6. Vault 36
Almost every vault in the Fallout universe comes equipped with food extruders that are designed to generate a variety of foods and sustain their populations. The food extruders in Vault 36 were designed to only provide it's dwellers with a thin, unpleasant gruel.
It's not clear what effect this had on the population of the vault, since its existence is not well documented, but it's safe to assume that most of the dwellers did not survive long, and that those who did were likely weak, malnourished, and susceptible to disease. They may have even resorted to cannibalism.
7. Vault 42
When Vault 42 was was sealed, no source of light brighter than a 40-watt bulb was included in the vault's inventory. The experiment may have been designed to test the psychological impact of poor illumination, or it may have been designed to cause the dwellers to adapt to low-light conditions.
8. Vault 43
Vault 43 is probably not consider canon, since it only appears in one panel in the "One Man, and a Crate of Puppets" webcomic that was made by the team behind Penny Arcade to promote the release of Fallout 3.
Vault 43 was intended to house twenty men, ten women, and one panther. It's never revealed what the experiment was designed to test, or what happened to the population of the vault after it was sealed, but it's probably safe to assume that things didn't go great for the dwellers.
9. Vault 55
Before Vault 55 was sealed, all tapes and forms of entertainment were removed. The experiment was designed to test how long dwellers could survive in isolation without any means of entertainment, and whether the lack of stimulus caused any lasting psychological effects. It may have also been designed to see what new forms of entertainment the citizens came up with to combat their boredom.
The experiment of Vault 55 was intended to run in conjunction with a similar experiment in Vault 56, and the outcomes of the two experiments were intended to be compared.
10. Vault 56
Vault 56 was almost the same social experiment as Vault 55, except instead of no entertainment, the dwellers were left with nothing but holo-tapes of performances from a particularly bad comedian.
The "Fallout Bible," which is the only source that mentions either vault, never really addresses the outcome of the two experiments, but it's assumed that the dwellers in Vault 55 lasted longer than the dwellers of Vault 56 before snapping.
11. Vault 68
Vault 68 was one of the larger vaults built for the sake of the experiments, and was intended to house one-thousand people. Of those one-thousand residents assigned to Vault 68, nine-hundred-ninety-nine of them were men, and only one lone dweller was a woman.
Vault 68 was not likely able to sustain itself for very long, since one female cannot provide enough genetic diversity to perpetuate humanity within the vault's confines. If the dwellers didn't find a way to escape before the vault automatically opened when living conditions above ground improved, Vault 68 probably only lasted a couple of generations.
12. Vault 69
Vault 69 was another large vault that was designed to run alongside the experiment in Vault 68, except of the one-thousand residents, nine-hundred-ninety-nine of them were women, and there was only one male dweller.
It likely suffered from the same genetic diversity problems as Vault 68, and while it's never revealed what happened to Vault 69 or its citizens, it's safe to assume that they didn't make it very far past the first couple generations.
13. Vault 77
Vault 77 is the subject of the webcomic "One Man, and a Crate of Puppets," and despite never making an appearance in any official Fallout game, it is considered cannon and is occasionally referred to within the universe of Fallout.
The experiment conducted within Vault 77 left one man alone in a vault with just a box full of puppets. As with many of the social experiments, it's assumed that the conditions within the vault were designed to test the psychological impact this sort of isolation would have upon its subject. It didn't take long for the dweller who would come to be known as the Puppet Man to escape his vault with his puppet and go on a murdering spree across the Wasteland.
A Vault 77 uniform can be found in Fallout 3 with an audio reordering from a slaver who implies that he's found a puppet and urges that it be burnt before the Puppet Man returns to claim it. The suit also happens to boost the melee and unarmed combat stats of its wearer, which is appropriate given Puppet Man's background.
14. Vault 108
Vault 108 began as a social experiment designed to fail catastrophically, but was brought down by an entirely different set of circumstances. When it was sealed, Vault 108 was meant to play out a little like Vault 34 and Vault 55 combined, with an incompetent, terminally ill Overseer, little security or management, no forms of entertainment, and an overstocked armory.
Despite being given every opportunity to devolve into chaos, Vault 108 thrived, and its dwellers began experimenting with cloning technology. A dweller named Gary was selected, and was cloned fifty-four times. Even though each of the clones ended up being physically identical to the original Gary, they were flawed, each going insane and lashing out violently against the vault's scientists, who were desperate to quell the force of the clones.
The clones eventually killed most of the population of the vault, other than those who managed to escape. One of the survivors was actually Gary 23, one of the many Gary clones, who found his way to a Virtual Strategic Solutions, Inc. facility in the Capital Wasteland where he was apparently killed for his Pip-Boy.
15. Vault 112
Vault 112 was designed to suspend its entire 85 person population in a series of virtual simulations for their stay underground. The virtual reality pods made the unwitting participants feel as though they were living perfect lives in idyllic places like the small, friendly cul-de-sac community of Tranquility Lane.
However, some time after the experiment began, Vault 112's Overseer Dr. Stanislaus Braun, who also designed the virtual reality experience, grew bored with the experiment. Instead of letting the dwellers live in peace, he started entering the simulation as a serial killer, virtually killing the citizens of Tranquility Lane until the entire population was dead. He would then wipe their memories, load the next virtual reality program, and start the sadistic process all over again.