i keep most of my fabric in two dressers. The one I prefer is the white Ikea one because the drawers slide in and out easily and are just deep enough to hold dollar-store shoeboxes. I don't put lids on the boxes but storing it like keeps everything upright. I fold the fabric in squares and line them up front to back in the boxes, by color. ROYGBIV-ly-like
My other dresser has very sturdy drawers, but they are longer, shallower, and don't slide quite as smoothly. I use it for my larger yardage, and scraps that have been cut to certain sizes in boxes.