Rammed earth is the one that I find fascinating. But I've not seen or heard much about it's use in the Midwest where winters tend to wet.
I did recently attend a workshop by Dr. Ronald Rael (Professor of Architecture @ Berkeley), and he mentioned that as concerns building with adobe bricks, with proper roofing, rain is a minimal to non-existent issue. I am not entirely convinced, however, and have also heard of solutions such as using “plasticure” on the outside of the walls.