From Diablo Wiki
A Stash is a chest where a player can store items. It is an important function in the Diablo franchise, since collecting items is a big part of each game. Characters can access their stashes from towns and cities in game, and the stashes are shared between all of the characters in the account, unlike in Diablo II where each character had their own individual stash.
It is important to note, however, that Hardcore characters do not share a stash with softcore characters, nor can they trade between each other.
The reason for the development team adding in a shared stash is to prevent characters from muling in drop games, where the battle.net servers may drop a player from a game, items may disappear, or a host of other issues. Put simply, it was not at all convenient or safe to trade items between characters on an account. Hence, the shared stash.
The stash is natively "unlocked" for the player. It doesn't have to be unlocked via a quest like the Cauldron of Jordan or the Nephalem Cube were. It is available as soon as the player enters New Tristram.
Upgrading the Stash
The stash is considered gold sink. The player begins with 7x2 (14 squares) of inventory space, which is equivalent to seven pieces of larger gear, or items which only take up one inventory space, such as amulets, or scrolls. The stash can be upgraded in 4 increments of 14 squares. Each set of two rows costs 10,000 gold each. After the player has maxed out the first page of the stash, they will be able to purchase an entirely new tab for a substantial gold cost. The tab begins the same as the natural stash: 7x2, and can be upgraded further, up to a grand total of 210 inventory squares. The total amounts per tab have been calculated during the Diablo III Beta test  and are shown in a table below.
The stash has three tabs in total, counting the first tab that the player receives for "free".
As the stash is shared, any character on the account has access to it, assuming that they are all either hardcore or softcore. Softcore and hardcore characters cannot trade items whatsoever. Yet, any character on a single account that peers into the stash will see the exact same items.
Below is a table showing gold costs per tab for the shared stash, but as these were taken during the beta test, they are subject to change for the game's final release.
|Tab||Tab Cost||Upgrade Cost||Total Cost|
Hardcore Death & The Stash
Hardcore characters do not have access to nor can trade with any softcore characters on the same account. If a Hardcore character dies any items they have placed in the shared stash will not be lost. All items on their person and inventory will however be lost with the character when it dies.
For archival purposes information on the evolution of the stashs' development is preserved below.
Diablo III has both the benefit and disadvantage of having completely random items. Pretty much everything can roll up different affixes, if not a range of its benefits. That's obviously great because the item hunt is what it's all about, more randomization means you can keep chasing that perfect item, but that means the amount of data needed to describe an item is much, much larger than say, a World of Warcraft item, which is static and only needs a unique number to identify it.
A Diablo III item first has to say the base item, then each individual affix that it rolled up, then the ranges of each variable, and if it has any sockets. And we have to think about everywhere an item can be, an item on the ground is still an item, and so is an item on the auction house.We obviously have room to grow if our projections are incorrect, or we just find that we eventually have the space. World of Warcraft definitely grew over the years, and that storage space didn't appear out of nowhere (although it does seem rather magical at times). We find three tabs to be plenty for at least the initial release of the game though. Not counting the items you're wearing (assuming they're the best you have), and assuming worst case scenario of nothing but 2-slot items, you'd be able to hold 405 swords per region. That's a lot. We don't expect people to be storing 405 swords... hopefully ever, because that might indicate you have an obsession with swords, but at the very least there should be enough storage to start and then we can continue to evaluate as we go.
An additional feature, which was a pleasant surprise to some, was the ability to select which class to view the stash as. Selecting a different class made the armor items appear different: each class has their own unique icons for armor. This also disappeared between Beta Patch 9 and Beta Patch 10. In the left image above the 'Appearance' tab can be seen and in the right hand image from January 2012 it has gone.
Shared stashes are confirmed as in the game and working, by an @Diablo tweet. 
In Blizzcon 2010's D3 Open Q&A Panel, RichterLocke from DiabloWiki asked if the D3 development team had decided whether or not to implement a shared stash. After some hesitation, Jay Wilson finally confirmed it: "Yes, and that's Blizzcon-exclusive by the way."
Jay Wilson spoke again about the shared stash at Gamescom in August, 2010. 
Also from Gamescom, Jay described the stash getting larger over the course of the game. 
The system remained undeveloped nearly two years later, as Bashiok explained in a forum post in July 2010. 
Finding and collecting items is a big part of the Diablo franchise, but storing and transferring those items has not always been easy. Jay Wilson spoke to this problem in BlizzCast Episode 5, August 2008. 
'''Bashiok:''' so in other words, I won’t have to worry about my game closing after...'''Jay Wilson: '''No, no more opening up a game, dropping items on the ground, and you know, hoping that the game stays open or getting a friend to help out, no more of that. You should be able to do it on your own.
- Got an Extra Million Gold Lying Around? - IncGamers Forum, 27-12-2011
- Hardcore and stash - Blizzard, 19/10/11
- Reduction of Stash Tabs - Blizzard, 1/2/2012
- Stash Tweet - Blizzard 12/01/11
- Jay Wilson Interview @ G4TV - Jay Wilson, Blizzard 28/08/10
- Jay Wilson Interview @ PC Games.de - Jay Wilson, Blizzard 20/08/11
- Shared Stash Still Just a Dream - Blizzard, 14/07/10
- BlizzCast Episode 5 - Jay Wilson, Blizzard, 28/08/08
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