Mariposa Military Base survived the fallout due to nuclear defense or something. Think there may be more underground shelters that aren't Vault-Tec? Underground military base like Black Mesa from Half-Life? Or guys who build bomb shelters in their backyards?

Well Lost Hills and the other bunkers the BoS tend to use were simply military bunkers not Vault Tech. Mariposa simply wasn't targeted. Hamilton's Hideaway in Fallout 3 was also a bomb shelter.

http://en.wikipedia.org/wiki/Fallout_shelter

^Well the real world government did build fallout shelters. And that is also before the Fallout timeline merging. There should be some.

As for Mariposa, it does have nuclear defense (from BOS entree in Vault)

They were protected by radiation, nothing is mentioned about bombs being intercepted. The base was experimenting with biological agents namely FEV. naturally it be sealed from the outside enviroment.

Sure there were bomb shelters that weren't Vault-Tec vaults. Remember that story from that female ghoul in Underworld? She says something about when the bombs fell, they were getting inside a bomb shelter and her dad stopped to help a lady when there was a flash. He was melted into the concrete and she changed into a ghoul later on. So these shelters weren't radiation proof, or they weren't big enough to have room for both survivors and food until you'd have to get out in the radioactive wasteland anyways.

No there aren't any non Vault-Tec Vaults, they're however non Vault-Tec Fallout Shelters or Bunkers.