http://fallout.wikia.com/wiki/Vault#True_purpose
As seen in the above link, most of the public vaults in Fallout 1/2 were secret social experiments organized by the Enclave to help them recolonize the US in the event of a nuclear war, with the few normal vaults like V13 being the controls in said experiment. This has carried over into Fallout 3, but a couple of things about the implementation bother me, namely
1: In Fallout 1 and 2, nobody other than the Enclave and Vault-Tec knew the true purpose of the vaults. The people living inside had no idea what would happen to them after the doors closed (or didn't close, in some cases). But if you dig around into the backstory for each of the FO3 vaults through audio logs/computers/etc you'll see the experiments were being carried out by their respective Overseers and his/her underlings. Why would anybody compromise the safety of their new home with strange and possibly dangerous experiments when the outside world as they know it (and Vault-Tec along with it) likely no longer exist? The Overseers were chosen long before the Vaults were sealed so I suppose you could argue they were prescreened for their willingness to go along with the experiments, but there's a huge problem with that line of logic in that
2) Fallout 3 is supposedly set some 200 odd years after the bombs dropped, and there are human survivors still living in some of the more ill-fated Capitol Wasteland vaults... which leads you to believe the experiments took place relatively recently. This only exacerbates the 'why would they do it?' issue. So the descendants of the original Overseers decided to go ahead with the experiments after hundreds of years? Even if their predecessors operated under the assumption that 'Big Brother' was still out and about after the nuclear holocaust and feared what might happen to them if they didn't cooperate, I'm pretty sure that the passage of 200 years would have convinced everyone in the Vault that nobody was coming to visit them either for good or ill.
Thoughts? I just read the thread about how little sense it makes for F3 to be set so long after the nuclear war and I have to agree.