I had the same question as StrixVaria -- what happens when you "deposit all collectibles" in your inventory.
However, I didn't completely understand the answers -- the two banks mentioned -- how do you access them?
Are they among the menus and windows, or do you go to a map location, or something else?
You can access your own bank (which stores items in separate tabs) from:
A banker NPC, which you can find in major cities. See: http://wiki.guildwars2.com/wiki/Banker
A crafting station. They (conveniently!) use the collectibles you have deposited until now. You can also manually withdraw them, but unless you want to sell them, I don't recommend it.
There is also an premium item allowing you to summon a banker anywhere.
For further information about your personal bank, see: http://wiki.guildwars2.com/wiki/Account_vault
The guild bank can only be accessed from specific NPCs. You will find them at the same place as the personal bank NPCs. See: http://wiki.guildwars2.com/wiki/Guild_Banker
As of the Queen's Jubilee's update, the Wallet has been introduced. The Wallet is a tab on the hero panel that tracks currency for each account. Things like gold, karma and dungeon tokens are stored there instead of on the Bank.
The Banks are both located in Lion's Arch and all the other racial cities, here are the ones in Lion's Arch:
