Nothing beats a dresser for storage. I use them for all kinds of storage besides just clothing. I have two kids dressers that I have filled with my stamps and another one just for stamping supplies. It's easy to pop open the drawer and flip through the stamps like records (or CD's).
Another favorite of mine? Paint! Paint is fabulous. It's relatively inexpensive and if you don't like it, just repaint. An dresser that your kids have outgrown can be transformed into a beautiful linen storage space. Just a little prep work and paint and you have something amazing.
Of course you are going to edit out items before you fill your new storage, right? You want to leave space so you can easily access your items.