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
Tiny, tiny 3D cubes. Reminds me of the good old pattern from k10k.
Source Etienne Rallion
Sounds French. Some 3D square diagonals, that’s all you need to know.
Source Graphiste
There are many carbon patterns, but this one is tiny.
Source Designova
A chequerboard pattern with a fruit theme. The fruits are from a posting by inkscapeforum.it.
Source Firkin
A free web background image with a seamless concrete-like texture and an Indian-red color.
Source V. Hartikainen
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Resa i Afrika, genom Angola, Ovampo och Damaraland', P. Moller, 1899.
Source Firkin
Alternative colour scheme to the original.
Source Firkin
Stefan is hard at work, this time with a funky pattern of squares.
Source Stefan Aleksić
This is the remix of "blue wave-seigaiha".This is the flowers of pink silk tree which is called "nemuno-ki".About pink silk tree ,refer to here:https://jp.pinterest.com/pin/500744052301210439/
Source Yamachem
A background pattern with green vertical stripes. A new striped background pattern. This time a green one.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
One more from Badhon, sharp horizontal lines making an embossed paper feeling.
Source Badhon Ebrahim
A seamless gray background texture suitable for use on websites. To me, it has the look of stone. Feel free to modify it to meet your needs (by making it a bit lighter or darker, for example).
Source V. Hartikainen
Snap! It’s a pattern, and it’s not grayscale! Of course you can always change the color in Photoshop.
Source Atle Mo
Prismatic Groovy Concentric Background 3 No Black
Source GDJ
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
Based on several public domain drawings on Wikimedia Commons. This was formed from a rectangular tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i
Source Firkin
A smooth mid-tone gray, or low contrast if you will, linen pattern.
Source Jordan Pittman