The first step to solving this problem of limited inventory space is to use your characters as mules. In my game, every single character has a secondary weapon equipped. Every amulet and belt slot is used. Both ring slots are filled. Not necessarily because the character is going to use those items, but because it frees up slots in my backpack.

The second step is to shell out for the backpack expansions. These are an ingame money sink. They partly encourage you to visit various merchants to see if they sell one of the precious backpack expansions. But they mostly force hard decisions about how to spend your money.

But then there's the third step. It's called Warden's Keep and it'll cost you seven dollars to download. It adds a new party camp that includes storage so you can free up backpack slots when you're adventuring. Bioware claims this was created after early reviews complained about the lack of inventory space. But rather than fixing the game by giving everyone a storage locker, they opted to use the problem as a way to make more money.