Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
From a drawing in 'Hubert Montreuil, or the Huguenot and the Dragoon', Francisca Ouvry, 1873.
Source Firkin
Embossed lines and squares with subtle highlights.
Source Alex Parker
This ladies and gentlemen, is texturetastic! Love it.
Source Adam Pickering
The act or state of corrugating or of being corrugated, a wrinkle; fold; furrow; ridge.
Source Anna Litvinuk
Abstract Stars Geometric Pattern Prismatic No Background
Source GDJ
After 1 comes 2, same but different. You get the idea.
Source Hendrik Lammers
The first pattern on here using opacity. Try it on a site with a colored background, or even using mixed colors.
Source Nathan Spady
Vector version of a JPG that was uploaded to Pixabay by theasad121
Source Firkin
Can never have too many knitting patterns, especially as nice as this.
Source Victoria Spahn
Prismatic Snowflakes Pattern 3 No Background
Source GDJ
Bit of a strange name on this one, but still nice. Tiny gray square things.
Source Carlos Valdez
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Dark, lines, noise, tactile. You get the drift.
Source Anatoli Nicolae
Seamless pattern inspired by a drawing on Pixabay. To get the tile this is formed from, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Light honeycomb pattern made up of the classic hexagon shape.
Source Federica Pelzel
ZeroCC tileable beechwood wood texture, generated in Neo Texture Edit by me. CC0
Source Sojan Janso
This one is rather fun and playful. The 2X could be used at 1X too!
Source Welsley
A seamless texture of worn out "cardboard".
Source V. Hartikainen
Remixed from a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
Black brick wall pattern. Brick your site up!
Source Alex Parker
Paper model of a tetrahedron. Modelo de papel de um tetraedro.
Source laobc
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
You know you can’t get enough of these linen-fabric-y patterns.
Source James Basoo
Prismatic Rounded Squares Grid 3 No Background
Source GDJ
If you like it a bit trippy, this wave pattern might be for you.
Source Ian Soper