My full sheets of paper are stored in some of the JetMax (? I think that's the name- they're the ones that Michaels and ACMoore sell- Michaels is substantially cheaper btw) stacked cubes. The top two have doors to help protect the papers from fading. I could only get a glass door on one of them so I just covered it over with a piece of heavy paper.
My 12x12" and print papers are in the top cube, first organized loose by color, then themes in sleeves, and then paper packs. This was redone a bit from last week after I found some plastic dividers I'd forgotten about.
The middle cube holds my 8.5x11" papers, again organized by color. I tend to keep them in the plastic they come in just to make it easier to grab a pack and move them around as I change my mind how to store them. :) You'll see there's one bag hanging out on top of the paper in that shelf- it's a scrap kit that I haven't decided what to do with- divide up or leave as is. Right now it's leave as-is and hopefully try to use in the next week or three. It seems to be the best place to have it right now since it won't fit in the top shelf and I want to keep it "doored."
Finally, the bottom cube is shelved and only the top area is for paper- actually just 2 thick packs that wouldn't fit in the top cube. The bottom of that cube holds my Big Shot and Nestability dies.