Paper

Iris folding - really nice stocking ornaments done with this technique

tea bag folding - make pretty rosettes, medallions and stars from teabags

cone ornament

paper embroidery Christmas ornament - reminds me so of my childhood - at the 70's this kind of thread-cat-craddle-artworks were very popular :-)
You could use the shrinkydink ornament forms from yesterday.

Paper ball ornament - origami style

another

icosahedrons and other forms you can make of old holiday cards and magazines and wrapping paper scraps and what not

Paper polyhedra

"Greek Paper Ball" - we used to make these of straw

"Super cool" paper star

snowflake tree ornament

Using the wrapping papers to make ornaments

Paper ribbon star

Woven paper hearts - with many patterns :-)

quilled paper ornaments

Martha Stewart makes a stacked paper tree - use bamboo skewers in stead of knitting needles.
If you don't have the polymer clay or such, you can make your own salt dough.
P.S. I don't like MS and I don't like "condoning" - or recommending - her site, but the craft ideas are great. Unfortunately. I love the ginger dough birds. *sigh*

and a really cute crocheted baby penguin - not of paper ;-D