I always construct a large natural stone Vault underground to store all of my valuables.
This time, it's under the second cavern, in the middle of a marble layer. The whole thing is smoothed and engraved, and guarded by two doors.
Inside is two stockpiles.
The first contains every artifact my fortress has ever made, with the exception of an artifact trap component that sits in a weapon trap in my front door.
The second contains a coin stockpile. I mint 3 or 4 different metals of coins every year to celebrate the turning of the calender year, usually gold and silver and then two other metals, somewhat randomly chosen.
The doors are kept sealed via mechanisms, connected to a lever that sits in my mayors room that only he can pull. Every year after the coins are done being minted, I have him pull the lever, and that year's artifacts and coins are taken underground to be sealed up and kept safely.
I think I might put some statues down there as well, my Dwarves just made a statue of this world's deity of gems and valuables.
What about you guys? How do you keep your artifacts? Put them in hallways so people can see them, just leave them around, or store them in a vault deep underground?
Bonus points if your vault is guarded with a solid wall of water or magma that has to be first taken care of with a complex obsidian making process before the things can be reached.