(covers information from several alternate timelines)
A safe or vault was a secure compartment used to protect the objects within it against theft or damage. Money or other valuable objects were typically placed within safes for this purpose. Safes were secured with a locking mechanism, which could be opened with a key, combination lock, or other technology.
A group of Ferengi led by Ulis demanded to know the location of the vault on board Enterprise NX-01 from Jonathan Archer after seizing the starship. They did not believe him when he denied such a thing existed, but used it as part of a ruse to regain control of the ship. (ENT: "Acquisition")
Captain Kirk had a safe in his quarters on the USS Enterprise, in which he kept his command packet and a record tape with his final orders to Mister Spock and Doctor McCoy should he ever be declared dead. (TOS: "What Are Little Girls Made Of?", "The Tholian Web")
Quark had a floor vault to keep his latinum, which his brother Rom broke into on at least one occasion in order to store the extra profits Quark's Bar earned while Quark was on a business trip. Rom replaced the damaged parts out of his own salary, and Quark did not notice; however, when Quark learned of this "treachery," he became angry and claimed Rom could not be trusted. (DS9: "Necessary Evil")
The casino within an altered version of Vic's lounge had a safe. As part of a scheme to return the holoprogram to normal after tripping a jack-in-the-box, Odo and Nog were required to break into the safe to steal the money within. This safe was secured with a combination lock, which Nog planned to break using his sense of hearing. However, it had an auto-relock tumbler designed to prevent just what he was attempting. Despite that, Nog was able to successfuly open the safe and get away with the money. (DS9: "Badda-Bing, Badda-Bang")