T.O.
We keep the boxed American Girl stuff in a folding fabric box from Target (about $6). Then I got doll clothes hangers (on eBay) and made a closet out of my husband's sneaker box w/ a hinged lid. We took 3 wooden skewers, wrapped them together with tape to form the clothes rail, and pushed the ends through the shoe box before taping the pointy ends, too.
Hair things and socks/tights are kept in ziploc baggies in the collapsible box.
The box and closet fit nicely on the bookshelf in my daughter's room.
I like the boxes better than the plastic drawers only for portability -- we can bring everything downstairs.