I have a long way to go, but I have positively identified examples of most of these fabrics, and I mean to grow the list and swatch samples. I hope that even the descriptions help others.
NETS
Illusion - Very fine, sheer net
Point d'esprit - Net with dots scattered all over
Tulle - Fine net with a hexagonal mesh.
LIGHTEST, OPEN WEAVE OR SHEER FABRICS
Crepe de chine - Plain weave with fine crepe effect
Gauze - Thin, sheer open weave of plain or leno weave
Georgette - Sheer plain weave with a fine crepe surface
Handkerchief linen - Sheer linen
Mousseline - Broad classification of lightweight, sheer crisp fabrics
Organdy - Sheer, plain weave stiffened lawn
Organza - Transparent, crisp plain weave
Voile - Sheer plain weave with crisp, wiry hand
FINE, LIGHT FABRICS
Batiste - Plain weave, with subtle lengthwise streaks
Cambric - Soft plain weave, slight luster
Challis - Soft plain weave, often printed w/ small florals
Charmeuse - Soft, drapey, smooth, semi-lustrous satin face, dull back
Crepe-back satin - Reversible satin weave, smooth & lustrous on one side, crepe on other
Gabardine - Twill weave w/ distinct rib
Lawn -Fine, plain weave, relatively sheer. Close construction
Percale - Plain weave, firm, balanced construction
Sateen - Cotton in satin weave
Surah - Silk or silky manufactured fabric in twill weave. Soft, lustrous
COARSER, HEAVIER FABRICS
Buckram - Plain weave, coarse, open, heavily sized, used as a stiffener interfacing
Cavalry twill - Strong, rugged, pronounced double twill at 63° angle
Cheviot - Hairy nap wool or worsted, rough surface, fulled. Plain or twill weaves
Chino - Twilled mercerized cotton
Denim - Right-hand twill weave, colored warp, white filling (compare to drill)
Drill - Resembles denim, but left-hand twill
Duck - Plain weave, light canvas
Homespun - Plain weave, course, uneven yarns, similar to tweed
Hopsacking - Same as burlap. Basket weave, coarse, loosely woven
Lodencloth - Coarse wool coating fabric woven in the Tyrols w/ natural water repellancy
Melton - Plain weave, completely smooth, short nap, at least partly wool
Muslin - Firm, plain weave cotton; broad category from sheer to heavyweight
Serge - Most commonly twilled worsted suiting dyed navy blue
Whipcord - Twilled rugged fabric w/ wiry hand
PILES AND TREATED FABRICS
Burn-out fabric - Made w/ 2 different yarns w/ pattern made by destroying one of the yarns in a printing process which uses chemicals instead of color.
Crushed velvet - Velvet processed to have irregular surface
Panne velvet - Flattened pile velvet
Plush - Surface longer than velvet, less closely woven
Velvet - Short cut warp pile fabric
PATTERNED OR PUCKERED TEXTURED FABRICS
Crepe - Wrinkled or grained surface effect
Embossed fabric - Raised design made by passing cloth through hot, engraved rollers
Matelassé - Puckered, quilted, waded effect
Plissé - Puckered stripes made by applying caustic soda
Seersucker - Puckered stripes made by weaving tension variations
SLUBBY TEXTURED FABRICS
Butcher cloth - Linen like, strong, heavy, plain weave
Donegal tweed - Plain or twill weave medium to heavy wool with colored slubbing
Doupioni silk - Irregular, rough silk reeled from double cocoons
Pongee - Plain weave, light to medium-weight irregular silk, often natural ecru color
Shantung - Rough, plain weave silk, heavier than pongee
VERY TEXTURED FABRICS
Bouclé - Woven or knit fabric using rough, curly, knotted, fancy yarn
Ratiné - Plain weave, loosely constructed fabric using curly, knotty fancy ratiné yarn
HORIZONTALLY RIBBED FABRICS
Bengaline - Plain weave, filling courser than warp, but more warp yarns used, covering picks
Broadcloth - Unbalanced plain weave, finer rib than poplin
Faille - Plain weave, like grosgrain only flatter rib
Grosgrain - Firm, closely woven plain weave ribbed fabric or ribbon
Ottoman - Plain weave, cords larger & rounder than faille or bengaline
Poplin - Subtle but noticeable rib warp plain weave fabric, more rib than broadcloath
Rep - Plain weave, close spaced narrow ribs, less than bengaline, more than poplin
Taffeta - Broad category of plain weave, fine, smooth, crisp fabrics, usually w/ fine cross rib
VERTICALLY RIBBED FABRICS
Bedford cord - Heavy, plain weave corded fabric
Corduroy - Pile ribbed
Pinwale corduroy - Finely ribbed
Piqué - Light bedford cord, or also in fancy patterns (i.e. bird..s eye)
FABRICS WITH SPECIAL FINISHES
Brushed fabric - Softened feel from wire brushing process
Chintz - Plain weave cotton or cotton blend w/ glaze treatment
Flannel - Light to medium weight plain or twill weave fabric, slightly napped
Moiré - ..Watered.. finishing process, usually applied to ribbed fabric
Polished cotton - Luster from satin weave, or smoothing roller finish
Suede cloth - Woven or knit fabric finished to resemble suede
Sueded silk - Soft nap finish silk
PRINTED PATTERN FABRICS
Calico - Plain weave cotton or blend with small, busy, printed pattern
Foulard - Lustrous twill w/ small printed design on plain ground
Toile de jouy - Floral or scenic designs, classic motifs finely detailed
WOVEN PATTERN FABRICS
Brocade - Rich, heavy jacquard-woven fabric w/ raised patterns emphasized by contrasting surfaces or colors (see jacquard, damask)
Chambray - Plain weave w/ colored warp, white filling
Damask - Similar to brocade, but flatter
Dobby weave - Specific, small, geometric figures in fabric woven w/ dobby loom
Gingham - Plain weave, even check plaid
Heather effect - Vari-colored effect from blended woolen yarns, often greens, browns
Houndstooth check - Twill woven in characteristic pattern
Jacquard - System of weaving capable of producing complex and large woven designs
Oatmeal weave - Uneven weave in small repeat which produces speckled surface
Ombré (woven or printed) - Gradual shading from light to dark, or hue to hue
Shadow stripe weave - Indistinct stripes produced by using different yarns, in a plain weave
Sharkskin - Most often blk & white in close plain weave worsteds
Ticking - Strong, durable, close woven in any basic weave, characteristic stripe
OTHER PATTERNED FABRICS
Batik - Wax-resist dying
Birds eye - Small indentations
Dotted swiss - Can be woven or flocked dots on plain weave
Eyelet - Edge-embroidered cut-outs or eyelets
Flock - Fuzzy pile decoration applied with adhesive, not woven
Honeycomb - A woven in waffle appearance
Ikat - Resist dying employing tying fabric
Waffle weave - Cotton in honeycomb weave
KNIT FABRICS
Double knit - Thicker knit, made in knitting machine with two sets of needles
Interlock - Thick, firm, double rib knit
Jersey - Single, plain knit
Tricot - Knit w/ pronounced crosswise ribs on back
MISCELLANEOUS
Lamé - Fabric w/ flat, metallic yarns woven in
These descriptions do not cover the fiber (i.e. wool, rayon, silk, polyester). Next time: How to tell the fiber from which a fabric is made.