These chairs, from the Terra Grass Armchair kit, are made from biodegradable cardboard forms. Simply fill the form with soil, seed it with grass, and watch it grow. I'm not quite sure how you would mow them, however.
Here is another collection of outdoor furniture, by 5.5 Designers, which incorporates plants into the design. I love the manicured hedge look of this design, although you can use flowers as well.
This Swedish Gustavian side chair was upholstered with shag carpet. I love the whimsy of this chair. In the most traditional environment, this chair would make a fun and unexpected statement! I have a slipper chair that I inherited and reupholstered once since college. I am seriously thinking about reupholstering yet again in a similar fashion.