DIY, craft, materials, and such / Fabrics - materials
Cellulose
Seed hair
Cotton
http://en.wikipedia.org/wiki/Cotton
Kapok
http://en.wikipedia.org/wiki/Ceiba_pentandra
Leaf
Manila
http://en.wikipedia.org/wiki/Manila
Sisal
http://en.wikipedia.org/wiki/Sisal
Bast
Flax
http://en.wikipedia.org/wiki/Flax
Hemp
http://en.wikipedia.org/wiki/Hemp
Jute
http://en.wikipedia.org/wiki/Jute
Ramie
http://en.wikipedia.org/wiki/Ramie
Proteins
Staple protein / wool
Wool is different from hair or fur in that wool...
- grows in staples, basically from from clusters of follicles
- is crimped, basically meaning it has bends and twists, which allow it to be spun
- is elastic (in part due to the above)
Sheep
http://en.wikipedia.org/wiki/Wool
Goat
Cashmere
http://en.wikipedia.org/wiki/Cashmere_wool
Mohair
From the Angora goat, but typically not called angora to avoid confusion with angora rabbit wool.
http://en.wikipedia.org/wiki/Mohair
Camelid
Alpaca
http://en.wikipedia.org/wiki/Alpaca
Llama
http://en.wikipedia.org/wiki/Llama
Vicuna
http://en.wikipedia.org/wiki/Vicu%C3%B1a
Rabbit
Angora rabbit
http://en.wikipedia.org/wiki/Angora_wool
Muskoxen
Silk
Silk is a filament protein, produced by certain insect larvae.
http://en.wikipedia.org/wiki/Silk
Natural polymers
...primarily cellulose.
Rayon
http://en.wikipedia.org/wiki/Rayon
Lyocell
Form of Rayon http://en.wikipedia.org/wiki/Lyocell
Acetate
http://en.wikipedia.org/wiki/Cellulose_acetate
Triacetate
http://en.wikipedia.org/wiki/Cellulose_triacetate
Synthetic polymers
There are many more fiber-like polymers that could be and are used. Below are some of the more common ones.
Polyester
http://en.wikipedia.org/wiki/Polyester
Nylon
http://en.wikipedia.org/wiki/Nylon
Aramid
http://en.wikipedia.org/wiki/Aramid
Acrylic
http://en.wikipedia.org/wiki/Acrylic_fiber
Modacrylic
http://en.wikipedia.org/wiki/Modacrylic
Spandex
http://en.wikipedia.org/wiki/Spandex
Elastoester
Fluoropolymer
http://en.wikipedia.org/wiki/Fluoropolymer
Melamine
http://en.wikipedia.org/wiki/Melamine
Nitryl
http://en.wikipedia.org/wiki/Nitryl
Vinyon
http://en.wikipedia.org/wiki/Vinyon