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?
Best Answer
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.