I have some rather large suitcases (too big for me to travel with now) that I use as storage units. The quilts stay clean--I also have a set of bookshelves in my sewing room I keep my newest finishes on. I have 3 boxes under the bed (bought bed risers so bigger boxes would fit under it). I keep the seasonal ones in a chest of drawers in the living room (really serves as my buffet). I also have five windows that I display quilts on rather than using drapes. I have light filtering blinds, so the quilts do not get damaged by the light.
I am preparing for a "Quilt-Christmas for for 2012" --my 22 family members will each get to pick a quilt to keep. I do this every 3 years or so--it clears out my space and I can begin to stockpile once again!