I have something that hangs on a door with compartments which works very well for storing my ribbons, bows and etc. It also stores large rolls of paper but the number it holds is limited. This allows me to keep everything in one place and I hang it on the inside of the closet door in our spare bedroom which is where I store gifts as I buy them.
But aren't gift bags wonderful? We also use gift bags and they circulate through the family so they get used again and again.