Pending on size, this is what I do....If the piece is still a full width of fabric it going back in the draw of color. If it is 'strippie' then I cut it into strips, 1-1/2", 2", 2-1/2", 3" for my string quilts, I have a Bankers box with nothing but assorted precut strings (good use of smaller pieces of leftover bindings). My favorate square size is 6", with that I can make a disappearing patch (4 or 9) or a twisted pinwheel. After those are cut what is left over I sort by both color and type (holiday) and use gallon size zip lock bags, these I then store in a labeled Bankers Box in my closet.
I like using the bankers boxes because they are inexpensive from Staples or Costco, are light weight and stack so well in my closet. At this point in time I probably have enough scrapes and stash to last two life times.....but as long as I keep them organized behind closed doors.....who cares.