I think I have tried so many different ways to organize... but here is my current system that I've used for the past year and really like it. My DH always tells me that I spend more time organizing than scrapping so I've been working on changing that.
I buy my paper in both stacks and in single sheets.
For stacks of cardstock, I tear them apart and then place each color (according to the rainbow) in a 12.5x12.5 inch baggie and hang it on my clip it up system. Any single sheets of cardstock are also filed this way. These are all on 1 Clip it Up floor model system.
Here is a link to what the clip it up systems look like: http://www.scrapbook.com/myplace/index.php?mod=gallerie...
For stacks of patterned paper, I keep them together (including the scraps) and file by manufacturer. I scan the front of each pack and keep an electronic image of them so I don't have to go pull them all our of their cases to know what I have (both IRIS and tall files). The photo below are the IRIS cases. http://www.scrapbook.com/galleries/543581/view /3501529/...
I normally buy single sheets of patterned paper by theme or thinking of it for a specific use. I use my second clip it up floor model to organize papers & embellishments by theme (for example, travel locations, Christmas, Fall, etc). I combine the single sheets by theme into 12.5x12.5 inch baggies and hang them organized by theme.
Its really a hybrid rainbow/theme system but it seems to correspond well to how my brain works and where I go to look for a piece of paper.
I should note that once in a while, I will tear out patterned papers from a stack, but they really have to be specific to a theme (for example, a seasonal paper pack will be split into Spring, Summer, Fall & Winter and then hung on the second clip it up.
I hope that helps!!