Each item requires only one square. However some smaller items such as scrolls and potions are stacked, which means that multiple items of same type can be stored in the same square (probably up to five each).
The inventory can also be extended with four additional bags, these can either be found or bought in the game. When you start the game (without any bags), you will have 12 slots, but with four large bags, you will be able to get up to 30 squares.
This is a detailed shot by Vikkz:
Inventory in Diablo 3.
There will also be a Stash facility but specifics of that have yet to be revealed.
Some fans would rather have an inventory with the multiple square items in the actual bag, but it's highly unlikely to change. Here is a quote from a discussion between a Battle.net member and Bashiok: [1]
- Phat_smoke: All items shuld = 1 inv square space
- thats my thot
- Bashiok:
- i totilly agre