The Vaults and the purposes they served (Taken from Fallout Bible)
Vault 8: A control Vault, intended to open and re-colonize the surface after 10 years. Vault City is the result. Unfortunately.
Vault 12: In order the study the effects of radiation on the selected population, the Vault Door was designed not to close. This is the Necropolis Vault... and the ghouls were the result.
Vault 13: Intended to stay closed for 200 years as a study of prolonged isolation, the broken water chip forced the Overseer to improvise and use the Vault Dweller as a pawn. Later study of the Vault 13 records by the Enclave led them to their current plan to end the war.
Vault 15: Intended to stay closed for 50 years and include people of radically diverse ideologies. Gathered from what you hear from Aradesh in Fallout 1, he has quite a bit of multi- cultural flavoring to his speech.
Vault 27: This Vault would be overcrowded deliberately. 2000 people would be assigned to enter, double the total sustainable amount. The location of this Vault is unknown.
Vault 29: No one in this Vault was over the age of 15 when they entered. Parents were redirected to other Vaults on purpose. Harold is believed to have come from this Vault.
Vault 34: The armory was overstocked with weapons and ammo and not provided with a lock.
Vault 36: The food extruders were designed to produce only a thin, watery gruel.
Vault 42: No light bulbs of more than 40 watts were provided.
Vault 53: Most of the equipment was designed to break down every few months. While repairable, the breakdowns were intended to stress the inhabitants unduly.
Vault 55: All entertainment tapes were removed.
Vault 56: All entertainment tapes were removed except those of one particularly bad comic actor. Sociologists predicted failure before Vault 55.
Vault 68: Of the one thousand people who entered, there was only one woman.
Vault 69: Of the one thousand people who entered, there was only one man.
Vault 70: All jumpsuit extruders fail after 6 months.
Vault 106: Psychoactive drugs were released into the air filtration system 10 days after the Door was sealed.