I keep everything big enough to cut something from. I don't pre-cut pieces but do sort my scraps by colour families into a couple sets of those plastic drawer sets that are see-through. I can easily see what colours are my favourites and which I use less often by how full the drawers are. Digging through for a project can be a bit of a pain, or it can be a nostalgic trip through previous projects, depending on my mood.
I have more trouble storing pieces that are full width, both yardage and partial pieces. I just can't figure out a good method for folding to fit into my cupboard.