I've been thinking about this because it's about to become an issue for me, since I'm running out of space.
Basically, I have a plastic bin with all my costumes in it. Each costume is in a large zipper storage bag so that all the parts are kept together. I used to just have them all loose in the bin, but I hated digging around trying to find all the separate costume pieces. So, now, they're organized, but I'm just about maxed out in the bin. I also don't have that much room to start a second bin...but I may have to.
So, what do you guys do with your clothes? Where, and how do you store them?