I like Vault 19, paranoia is a funny messed up tool.

Vault 21 from New Vegas has to be my favorite. I love to whole idea of a symmetrical vault where everyone has the same things. No one is better off than the next vault dweller. I also just really love the design of the dinner.

In Fallout 2 would be Vault 13 (obviously populated by Talking Deathclaws)

Also Vault 15 and his inhabitants (Khans) which were gun-raped twice, by "The Vault Dweller" and his descendant "The Chosen One", that's a shitton of bad luck, lol.

For Fallout 3 would be Vault 108, man it's just hilarious going there and shoot at those screeching clone bastards  

Gaaaaary...:

In New Vegas is Vault 34, just for the difficulty and how a radiation leak can fuck up all. 

Also the goddamn Vault 22, oh boy the first time i went there, those spore carriers spooked the shit out of me, and now i find the place very easy to beat, i wish there would be more "spore" kind of enemies in the mojave.