How do you store & organize PATTERNED PAPERS?

First, I organize by color.
Multi-color is organized by pattern (stripes, dots, grunge, watercolor, checkered-plaid, wood, brick, etc..).
A few papers are organized by brand (Basic Grey, Daisy D's, etc..).

I keep cardstock in rainbow order but I don't have anywhere near as much organisation for my patterns. As my pp stash has grown I've kept my CVS papers together, and a lot of my FJ papers are near each other in my stash as I typically bought during sales so would have nothing new for a long time, and then several collections worth of paper at once. My paper is stored in a set of drawers on my desktop and in two Iris containers, but other than those two my stash is pretty random, as I prefer not to have it sorted, so brands and collections (where I have more than one piece of it) will be completely mixed up.

same as lg... rainbow order... multi color in its own section... i break up the collection as soon as ive used it and then it all goes into my random color order...

I have Iris containers that hold 12x12 paper.

Pink one is for dd's paper.

Blue one is for ds.

Clear one for fall/Halloween.

Clear one for winter/Christmas.

I do not separate by color or brand.

I just file through and grab what speaks to me.

I also mix and match across lines and companies.

The containers are stacked in a cube in my desk.

This is basically how I organize mine as well except I keep all of them in vertical paper organizers in a repurposed computer/tv armoire in my craft room. I don't organize them in alpha order within the themes but otherwise I pretty much do the same! 
Most older lines I keep all together (Basic Grey, October Afternoon) and sort by collection.

by company. most are in large containers on top of a cabinet where i can stand and leaf through them easily. 

I organize by color using Totally Tiffany 12x12 Paper Handlers - five of them fit perfectly into an IKEA Kallax cube. I use four that are split up in ROYGBV-ish and one for multicolored that don't have a predominant color. That one is split by: stripes/dots, other shapes, inanimate objects and things that are alive. I really like this system - it works well for the way I create.

My patterned paper is stored in huge mix of different ways. I have some theme categories, mostly Christmas, travel, and fall. A bunch of it is by collection. Everything else is sorted by papers that I think would work well together to make a page. I guess you could call it page kits, but I don’t really think of it that way. After I have used the majority of a collection or all those one off sheets of paper I end up buying; I loosely sort them together in plastic envelopes. It ends up being a really unorganized bunch of paper; but I can pull one and usually manage to make a page. 

The majority is stored by kit or collection. Kits are in labeled kit bags and collections are in labeled iris containers. Just the name of the kit or collection is enough to let me know what is inside. My brain is weird like that.

My "one-off" papers are stored by color. These are individual papers I bought because I like them, but not the entire collection, or are left overs from kicked collections or kits. They are stored in Totally Tiffany paper holders. This is true for both 12x12 paper and 6x6 papers.

I have a small stash of papers are are very themed: baby, kids' activities, school, seasons, my childhood (new theme, setting aside retro 70s and 80s feel papers) are my only themes. These are stored in individual bins with themed embellishments.

I feel overall it works for me. I mostly pull what grabs my attention and use it, so I don't feel I need to know exactly where every piece of paper I own lives. However, there are times I wish I could use my paper with more versatility and creativity, but I am not about to sit down are reorganize it all. Playing around with it, I can't come up with a possible plan that really allows that to happen. I don't want to spend the small amount of time I have to craft organizing rather than making.

All of my paper is stored in Cropper Hopper Paper Keepers, sorted by cardstock and patterned paper. Cardstock is sorted by color and patterned paper is sorted by theme, collection, or color. Christmas/baby/Valentine/Fall, etc are by theme. Polka dots, stripes, or other basic graphic designs are sorted by color. Collections are together with a divider separating them in the paper keepers, so each paper keeper probably has 25 or so collections in each one. It's really easy to find exactly what I'm looking for.

The exception is 6 x 6 paper pads. Those are stored in two bins on the bookshelf and sorted by occasion (birthday, baby, Christmas, Valentine, etc) where I can flip through them.

I keep my paper sorted by manufacturer and stored in vertical paper holders in my Kallax.

I mostly scrap by collection, so I keep collections together. They're sorted into themes and then by manufacturer. I keep them mostly in record sleeves or 13 x13 ziplock bags for the bigger collections. I keep the collections in bins like the 13 inch Target cube ones. I have some older fabric bins with a wire frame, too.
6x6 pads are with the collection or in a mini Closetmaid cube organizer

I  agree.
There no such thing as insane amount of paper. 
There's no such thing as too much paper.
There's always room for MORE paper. 

PaperAngel, can we use a loose definition of "organized"?
I keep collections together until they're mostly used up and then file papers with the rest of my papers organized by color (or theme).
Papers are kept in Artbin containers. Which makes the paper stored flat. Not the handiest but I tried the vertical storage containers and found them frustrating to deal with. Plus the dust issue.
And I figured that if I ever used up most of my paper (HaHa), I could use the containers for lots of other things.