In Borderlands for the PS3, Xbox 360, and PC, you have limited inventory space to store your items. There is a way around this however, exploiting the coop system.
Start a game with the character that you want to store items with. Now create a coop game, and sign in with a different controller creating a new character. Drop the items and have your new character pick them up. Now exit the game with both players, making sure to save both of them.
This might not be the best storage option, but it will help in a pinch, and it’s especially handy for storing items you rarely need or can’t use yet.