Not that long ago, knitters were mostly limited to wool and acrylic. The yarn industry now provides a wide range of fibers, from the highly exotic to the highly synthetic. While the variety is wonderful, it can also be frustrating to separate meaningful information from hype. Here are most of the yarn fibers that you'll find, on their own or blended. Except for Wool, the list is sorted alphabetically.
Wool
Natural animal fiber spun from the fleece of sheep. Other animal fibers are often called "wool", but for precision, I'm listing those separately. For me, wool means sheep.
Characteristics: wool comes in a variety of softness and fiber length. Elastic and light. Some wool very fine, some very hairy. Feltable unless treated to be Superwash.
Advantages: often affordable, long-lasting, warm, forgiving for the new knitter. Stays warm when wet.
Disadvantages: some wool can irritate some skin. Some people are sensitive to animal fiber in general, others have an allergy to lanolin which is only found in sheep's fleece.
Wool variations you might see on labels:
Merino: Merino wool comes from the Merino breed of sheep and is considered one of the softest wools. You will see categories of Merino: fine, superfine, extrafine, supersoft, New Zealand.
Shetland: from the Shetland breed of sheep; fine and soft.
Peruvian or Peruvian Highland: comes from the Peruvian Highland sheep, a cross between Merino and Corriedale. Soft and inexpensive.
Lambswool: wool from a young sheep.
Virgin wool: a grade of wool meaning either that the wool comes from the first shearing or that the wool was spun for the first time rather than recycled.
Superwash: wool that is treated or coated to make it machine washable.
Acrylic
Synthetic polymer fiber made from polyacrylonitrile.
Characteristics: comes in a wide variety of textures and colors, feel soft to the touch.
Advantages: inexpensive, washable, non-irritating. When blended with other fibers, add lightness and durability.
Disadvantages: after washing, can look shiny, often pills.
Alpaca
Natural animal fiber from the alpaca. (What's the difference between a llama and a alpaca? Alpacas are smaller, and are raised specifically for their fleece).
Characteristics: long, fine, fibers, often looks slightly "hairy". Feltable.
Advantages: Warm. Soft. Baby, suri varieties very soft. Contains no lanolin.
Disadvantages: Like wool, can irritate sensitive skin.
Angora
Natural animal fiber from the hair of Angora rabbit. (Not to be confused with Mohair, which comes from the Angora goat.)
Characteristics: very fine and soft.
Advantages: downy soft, makes pretty fabric with a halo.
Disadvantages: pricy, needs special care.
Bamboo
For most Bamboo listings on a yarn label, you should see Rayon. According to the FTC, fiber content labels should specify "viscose from bamboo" or "mechanically processed bamboo." The first, and most commonly used, is viscose rayon made from bamboo cellulose. The second is fiber spun from the bamboo plant. For more information, see this link from the FTC.
Camel
Natural animal fiber from the undercoat of the Bactrian camel.
Characteristics: tan colored. Light weight, fine, soft.
Advantages: very soft, luxurious.
Disadvantages: expensive, limited color selection.
Cashmere
Natural animal fiber from the undercoat of the Cashmere (Kashmir) goat.
Characteristics: very light, very fine, very soft. Easy to work with. Has soft halo.
Advantages: soft, lightweight, non-irritating, luxurious.
Disadvantages: expensive, delicate.
Cotton
Natural vegetable fiber made from the cotton plant.
Characteristics: typically dense and less elastic than wool. Texture ranges from rough to glossy.
Advantages: does not irritate sensitive skin, washable, suitable for warm weather. Has great stitch definition. Inexpensive.
Disadvantages: can be heavy on the hands, and is unforgiving on mistakes and uneven tension. Large garments can be heavy and stretch. When washed, some cotton shrinks dramatically.
Variations you'll see on labels: Pima (soft), Egyptian, mercerized (shiny).
Donegal Tweed
This can have two meanings. As a yarn name, it means that the yarn looks like Donegal Tweed fabric, which is characterized by its earthy, dense colours, and wool slubs. As a fiber listing, "Donegal Tweed" is a synthetic fiber slub blended into yarn to make it look like Donegal Tweed fabric.
Hemp
Natural vegetable fiber from the hemp plant.
Characteristics: matte, highly textured, inelastic.
Advantages: when blended with other fibers, soft to the skin. Durable. Touted as eco-friendly. Usually machine washable.
Disadvantages: can be hard on hands.
Linen
Natural plant fiber made from flax.
Characteristics: matte, slightly grassy texture, inelastic.
Advantages: when blended with other fibers, soft to the skin. Durable. Good for warm weather. Often machine washable and dry-able.
Disadvantages: can be hard on hands, sometimes sheds as you knit, or when wearing.
Milk
See Rayon.
Mohair
Natural fiber from the hair of Angora goat. (Not to be confused with Angora fiber, which comes from the Angora rabbit.)
Characteristics: very light weight, long hairs. The softness of mohair varies. Kid mohair is softest. Feltable.
Advantages: a little goes a long way, makes a featherweight open fabric.
Disadvantages: can be itchy to the skin.
Nylon
Synthetic polymer fiber derived from petroleum.
Characteristics: often seen blended with wool (especially in sock yarn), or used in novelty yarns.
Advantages: strong, dyes well, drapes nicely, inexpensive.
Disadvantages: tends to be inelastic, melts in contact with heat, can hold on to body odors.
Polyester
Synthetic polymer fiber derived from petroleum.
Characteristics: often used in novelty yarns (like eyelash yarn). Sheen ranges from dull to satiny.
Advantages: can add sheen or novelty elements (sequins for example) to yarn.
Disadvantages: can feel synthetic to the touch.
Possum
Natural animal fiber from the fur of possums.
Characteristics: usually seen blended with wool. Grey in color.
Advantages: Soft to the skin. Very warm. Often sold as part of fundraising campaign.
Disadvantages: No color selection. Not widely available.
Rayon, Viscose Rayon, Viscose derived from ...
Semi-synthetic fiber spun from chemically treated and extruded plant cellulose or proteins. Soy, Bamboo, Milk sound Natural, but they are semi-synthetics.
Characteristics: silky feel, heavy, sometimes shiny.
Advantages: drapes nicely, lustrous, soft on the skin. Inexpensive.
Disadvantages: inelastic to work with, stretches when wet, can become shiny. There are some concerns about the environmental impact of rayon production and the overhyping of eco versions of rayon.
SeaCell
See Rayon.
Silk
Natural animal fiber spun from the cocoons of silk worms.
Characteristics: typically dense and less elastic than wool. Texture depends on how the fiber is processed. Ranges from matte and textured to glossy and smooth.
Advantages: does not irritate sensitive skin, suitable for warm weather. Has great stitch definition. Drapes beautifully.
Disadvantages: can be expensive. Some question regarding the ethics of harvest methods.
Soy
See Rayon.