Roll 'em

I love gift packaging, but I also find it very wasteful when they're just thrown away after the gift is opened. So I always try to reuse gift bags and ribbons. To store used ribbons—and stretch them out at the same time, without having to iron them—I roll them around the cardboard cores of toilet paper.  Depending on the width of the ribbon, each core can accommodate one to five ribbons.
  I anchor one end with a small piece of adhesive tape onto the cardboard then start stretching and rolling. The other end needs another piece of adhesive tape, of course. A word of warning: resist the temptation to roll the ribbon perfectly parallel to itself and to its neighbors. The point here is to store the ribbons neatly for reuse—and quickly enough so it doesn't feel like too much of a chore that you end up just throwing them away because keeping them is a bother.

I also keep cords, string, and yarn, but they don't require stretching, so I just loop them then tie them into very loose knots.
  The ribbon rolls are carefully stacked when I store them, but the loops of cord get carelessly tossed into one box.