I have to admit that I am feeling like a genius here, having solved the problem for all time of how to store gift wrap. Previously my rolls have been unrolling and lolling about on an entire shelf, but no more. I bought a really cheap vinyl over-the-door shoe hanger, and hung it up inside the closet. Then, with a utility knife, I cut out the bottoms of all the pockets but the bottom row. I slid my rolls down through all the pockets and stuck their ends in the intact pockets.
The hanger was tall enough to do two stories of this, so I can store lots and lots of rolls in no space at all, and they stay in good shape.