In what setting? Makes all the difference. An Eberron bank that was a brnach of House Kundarak would be a heck of a lot different then am underground bank for rebels and shadowy types not under the eye of the Sorcerer Kings in Dark Sun vs. a Dwarven Clan's bank in FR that's not open to non-dwarves.
Fair point. I’m usually thinking about Forgotten Realms, since that’s become the default setting for D&D.
Thanks for all the responses thus far, you have given me lots of great feedback!