Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
A dark pattern made out of 3×3 circles and a 1px shadow. This works well as a carbon texture or background.
Source Atle Mo
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
This background pattern looks like bamboo to me. Feel free to download it for your website (for your blog perhaps?).
Source V. Hartikainen
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
Medium gray pattern with small strokes to give a weave effect.
Source Catherine
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Nice little grid. Would work great as a base on top of some other patterns.
Source Arno Gregorian
Formed by distorting a JPG from PublicDomainPictures
Source Firkin
"Beige Stone", Tileable Texture.
Source V. Hartikainen
Derived from a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857. The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
A seamless pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin