I keep mine in a plastic tote to keep the light and air from it which both can cause the thread to deteriorate.

I have an antique steamer trunk that still has its inserts. I store all my thread in the inserts and the bottom half of the trunk I store wide back yardage, my pantos and I keep my flannel stash stored there as well. This keeps the thread protected and out of direct sunlight. It also keeps me from expanding my thread stash too much. When the inserts are full I won't order thread unless I need a specific color for something.

I bought a plastic dresser from Wal-Mart and keep mine there. I also have some in the plastic drawers that you can buy and stack.