Since it's the season of giving, it's also the season for wrapping. I enjoy the art of giftwrapping, but I loathe the storage part. My rolls of paper always seem lost and/or crushed (generally under my bed), and my closet isn't large enough to hold one of those trash can-type wrapping paper holders. This nifty hanging organizer ($19.99) could be the answer. It hangs vertical in your closet and has clear storage pockets to hold cards, tape, or tissue, etc.. There's a pocket for bows that has a diagonal slot for easier access, and there's a ribbon pouch that has a horizontal pouch so they can be dispensed right from the organizer.
Velcro straps hold the rolls in place, but can be released when needed. They also keep the rolls upright. The whole thing can also simply lay flat and slide under a bed. Available at the Container Store.