I had a quilt box made by a friend's husband who is an experienced carpenter. It is beautiful, and holds lots of quilts and quilted items.
I will admit; they are folded, but I take them out every few weeks and change the wall hangings around, thus also re-folding them in the process. I also layer them on the beds, but I love my quilt box, and have had many compliments on it.
Our guild emphasized not to ever store them in plastic for the same reasons the girls in above posts stated.
Mariah