I mostly make modular origami (More than one sheet of paper folded into units which are put together), because it's much more interesting. Heres some of the better stuff I've made and bothered to photograph. All of these are other peoples designs.
(click on the photos for a larger picture)
A great site to visit if you're interested
Satomi taught me this variant. Two extra folds on a Sonobe unit produce the white triangles.
Just as the title says, it's six intersecting square frames...Maybe I'll take a better picture...
Same Basic Idea as the Icosahedron below. 90 1x8cm strips of paper and 180 1x4cm strips of paper. Lots of cutting...ugh... The second picture shows how small this thing is. Putting in the last few pieces was crazy hard.
Based on the tetrahedron by Francis Ow. The model pictured below recently fell apart, so I made one with thicker paper and it looks a lot nicer. Pictures soon.
Snapology is a really easy system that can be made in to pretty any polyhedron. Strips of paper are folded with crease lines at intervals to make 1:1 squares in the strip. Basically, 1:2n (n is the number of sides on that shape) strips of paper are folded into the shape you want for one face of the polyhedron, and 1:4 Strips (here, the black) connect two pieces together.
12 Sheets of paper w/ different colors on either side are used. I Couldn't find enough of one type of double colored paper, so I made my own with glue.
At least, I think it stars with a T.... I can't remember. Gah, when I took this off the shelf all the joints came loose...
I got this from a book called 3d-Origami. You use thousands of a simple triangle unit and put them together. I think the unit is somewhere on the internet...
VERY weird. Check out Extreme Origami at a book store. Take a large relatively stiff piece of paper (I use strathmore art paper, comes in tabs of 40 sheets) and score with a compass in concentric circles. Score both sides, but don't rip through the paper. Cut out the circle and the inner circle, and alternate valley and mountain folds on the score marks. Now you can bend it into weird shapes, combine them like I did below, or burn them....or not....
Experiment with different sizes of inner circles.
One unit.
Two units.
This thing is very interesting at all angles.