Iris folding - really nice stocking ornaments done with this technique
tea bag folding - make pretty rosettes, medallions and stars from teabags
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
icosahedrons and other forms you can make of old holiday cards and magazines and wrapping paper scraps and what not
"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