I use these paper products from everything from sub-walls to the building themselves. I did a mini-series on business card structures and have used cardstock for shingles, clapboards and individual boards.
Outside of a few index cards and Strathmore board, the majority of materials were fished out of the recycling bucket. Most of it is from mailers, stiffeners, and packaging materials. The supply is practically endless.
Outside of the index cards most of these materials measure about 1mm thick and are pretty sturdy in their own right. However, even when using glue sparingly the structures components have a tendency to warp and must be weighted when waiting for them dry and braced from the inside when assembling.
As with the business card structures I sometimes choose a particular sized material, just to see what is possible.