I have the plastic drawer chests. I have them in a closet and the material is sorted by color. I like that they're protected from dust and sun.

I have 8-10 20 gallon tubs of fabric in my small sewing room. Some tubs are in the small closet, some are under tables and some stacked againist the wall. But I have labels on the outside by color, vintage stuff & novelty/baby as I make alot of charity quilts. Most tubs are not clear but I am too cheap to buy new tubs. In fact I advertised on Craigslist looking for cheap clean tubs and paid only about $15 for all. Yes, I am poor & cheap but rich in spirit!

If you are going to store the fabric on open shelves, keep it from any sunlight direct or indirect. I stapled a pretty cotton shower curtain (clearance at Big Lots) to a wood book case years ago and would flip it out of the way when I wanted to pick fabric. I now have shelves in a closet 24" apart and had my LQS save the cardboard sleeves that the fabric comes wrapped on. 3 shelves of 24" high, the other half is 3 shelves of 18" for folded fabric and fat quarters. on the floor are plastic bins (smaller ones as the big ones filled with projects, kits are too heavy for me to lift) with whatevers.

I have many drawers and store by color.

I went to the store and got the bookshelves w/the cubbies; there are nine cubbies in each; I stacked two rows two high. Some of them have the canvas cubes in them to hold projects, patterns, notions, etc. Others have nothing so that I can put my stash, batting, etc in them. I try not to keep a really large stash so this works really great for me. I also have alot of fleece and that I keep in totes under my cutting table I got from JoAnns 1/2 price.

I have a bookcase, then I have clear plastic totes (IKEA, Container Store, sometimes Walmart) for the fat quarters, and a few fat eighths, each color in a separate tote. Because they are clear, I can see the colors, but the fabrics are protected from dust, pet hair, whatnot. I have 1/2 yard lengths also this way.

I have a pretty large stash...the majority of mine is stored in crates turned on end and is by color, crates stacked 4 high, with a curtain in front to keep out sunlight...the crates are within a closet. Light colors/backgrounds are on the shelf above, with a piece of muslin draped over again to keep out sunlight.
Then I have another cupboard full of larger pieces of fabrics for borders and backings. And one dresser upstairs full of plaids, another full of batiks, florals and more plaids. Plus another tub of more plaids that don't fit (yet) into the other storage areas. I hope to keep using my plaids enough that all will fit into drawers soon.

Even room light can fade fabrics, not just sunlight, so try to keep your fabrics covered some way so they don't fade!

Stash is inside a closet on shelving. I do keep my precuts tied with ribbons in a basket sitting pretty on the old treadle.

I store mine in the 9 cube containers from Target. There's no light at the end of the room that the fabric is in, but I do put an old sheet over it when not in use.

I have 2 of these containers and a small dresser that holds my batting and some other fabric that didn't fit.

I keep mine color grouped in clear plastic sweater or shoe boxes on bookshelf.... works great ...