This background pattern contains a seamless texture of bark. It's not very realistic, but I think it looks quite nice.
Source V. Hartikainen
A slightly more textured pattern, medium gray. A bit like a potato sack?
Source Bilal Ketab
This is indeed a bit strange, but here’s to the crazy ones!
Source Christopher Buecheler
Turn your site into a dragon with this great scale pattern.
Source Alex Parker
A seamlessly tile-able grunge background image.
Source V. Hartikainen
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
A lovely light gray pattern with stripes and a dash of noise.
Source V. Hartikainen
Alternative colour scheme. 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
Prismatic Polka Dots 3 No Background
Source GDJ
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
From a drawing in 'Kingsdene', Maria Fetherstonehaugh, 1878.
Source Firkin
A seamless chequerboard pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
Prismatic Groovy Concentric Background 5 No Black
Source GDJ
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
A seamless pattern formed from background pattern 102
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Nasty or not, it’s a nice pattern that tiles. Like they all do.
Source Badhon Ebrahim
Prismatic Hexagonalism Pattern No Background
Source GDJ
Abstract Ellipses Background Grayscale
Source GDJ