Note Printing Australia has developed the technology for creating plastic "paper money". Most of the notes are smooth clear plastic with intense and high resolution coloring. They usually have a small see-through window with a watermark-like design in it. The Australian 10 dollar note from 1988 actually contains a hologram (but not a very good one). Lots of people don't like plastic notes because of they can be difficult to handle. See section on dealers for address of Note Printing Australia.
There are also Tyvek plastic banknotes (I've seen one from Haiti) which are a lot more paperlike in texture. Tyvek is the kind of plastic used in those slippery fiberous plastic indestructable Federal Express envelopes.
Some countries with plastic banknotes: Australia (4), Singapore, Western Samoa (2), Papua New Guinea, Kuwait, Indonesia, and Isle of Man.