I use stacks of Sterilite plastic drawer-bins and they're great EXCEPT that I have them very full now and they're getting so heavy that it's getting hard to open and close the ones on the bottom. Booo!
I'm contemplating building some sort of framework so only one or two drawers are in each 'cubby', thereby saving a lot of pressure on the lower drawers. I really like those drawers; I even have figured out exactly how to fold my fabric to make it fit perfectly so I'd hate to get rid of them. (Not to mention how much I've paid for the darn things!) I have cats and I don't trust them to stay away from a bookcase full of fabric, even if I have a curtain over the front. I'm SURE they'd end up sleeping in my stash, the little monsters!!
Maybe some day I'll get the space and finances to invest in some real armoires for my fabric. That would be glorious.