I know I wouldn't be able to cope with a stash I couldn't see, so my stash is limited in size by the shelving I have available. I fold my fabric as I do when cutting it, and then fold it down one more time, and then fold that narrow piece in half or thirds or quarters (depending on its length), and then stack them on shelves by color with the fold facing out. Fat quarter bundles I keep together on a separate shelving unit in the hallway. Pieces larger than 2 yards I keep together on a bottom shelf. My stash is mostly in half yards and yards.
Scraps are another matter. I don't really have a working system for scraps. While piecing a quilt, I throw scraps in a dresser drawer. When the drawer is full, I empty it into garbage bags, which I keep on my bedroom closet floor. When I'm looking for something in particular, I dump the garbage bag out on my bed. Not an efficient system to say the least, lol.