Gift Bags

Actually I'm storing mine on hangers in the closet and it's worked great for years. I have the biggest bags on the hangers, then the other bags inside, sorted by size and next to each other. I have one for baby showers and little kids, and another for birthdays and holidays. I keep it to the far right of the closet, out of the way, and it always takes just a minute or less to find what I need.

Mrs. On Purpose folds them and puts them in the largest gift bag - and that is in a basement closet (out of the way).

The tissue paper tends to get stuffed into one of the bags and set next to the bag 'o bags.

It sounds like your system, because I am usually told that I picked the incorrect bag anytime she sends me to retrieve one. "Well, I really wanted the red and purple one from my birthday 4 years ago..."

I have hooks, all along the wall of my storage closet, where there are no shelving. So any bare space on the walls, I have hooks. Those stick on hooks.
On these hooks, I hook on a handled grocery bag, and put all these gift bags/gift wrapping things in it.
And it works.
And I am thus also utilizing the walls, with hooks, in the storage room too. Which utilizes space, better.

GrammaRocks, also has a great similar idea!

One handy hint about the tissue. You can hang it with pant hangers and it is easy to keep wrinkle free, or wrap it around a card board tube and tie it with a ribbon.. Also wrinkled tissue paper can be ironed flat..

Ido like gamma and have one big bag I keep them in and have it hanging.

My gift bags are in a plastic tub. My tissue paper is coordinated by color in matching small colored bags hanging on command strip hooks. My ribbon is a story for another day. My wrapping paper is hanging on the ceiling of the closet. I attached command strip hooks to the top of the closet wall (4-5 inches below ceiling). Then I strung twine across in three rows. Laid my wrapping paper rolls across it. Ta da lots of room to move around and I can reach it no prob.

Yes, I am a craft-aholic and I should probably attend meetings somewhere...

I have a plastic 3-drawer thing on wheels.
One drawer holds gift bags.
Another drawer holds folded tissue paper.
Bottom drawer has random things: flattened boxes, tape etc.

On top sits several paper towel holders (the kind that stand on end that
usually sit on kitchen counter) holding spools of ribbons. They trick was
finding a paper towel holder w/a small enough paper towel holder dowel
to fit through the spools of ribbons. The ones that don't fit go in the
bottom drawer.

You could always get a cloth shoe and pocket holder that hangs over closet doors. Those work great for storing stuff. The pockets on some of them are really big so you could fold up and put the gift bags in there while the ribbons and things can go in the smaller slots.

big plastic storage bin

I have a storage box that would fit under my bed however, its down in my basement. Its a wrapping paper storage box. I used to use it for wrapping paper but found most Christmas wrap was too long for it. Now I just use it for my bags and my wrapping paper is just set on a shelf. :(

Mine are in a box, laid flat. I just sort through them when I need one. The ribbon and tissue are in a large gift bag next to the box and all of it is stored in the basement.