This background pattern looks like bamboo to me. Feel free to download it for your website (for your blog perhaps?).
Source V. Hartikainen
A white version of the very popular linen pattern.
Source Ant Ekşiler
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
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
Background formed from the original with an emboss effect.
Source Firkin
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Prismatic Isometric Cube Extra Pattern No Background
Source GDJ
8 by 8 pixels, and just what the title says.
Source pixilated
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
Source Firkin
Submitted in a cream color, but you know how I like it.
Source Devin Holmes
Light gray paper pattern with small traces of fiber and some dust.
Source Atle Mo
Derived from a corner decoration itself found as a jpg on Pixabay.
Source Firkin
A seamless pattern formed from a rectangular tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Dark, lines, noise, tactile. You get the drift.
Source Anatoli Nicolae
CC0 and seamless wellington boot pattern.
Source SliverKnight
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Little x’es, noise and all the stuff you like. Dark like a Monday, with a hint of blue.
Source Tom McArdle
Never out of fashion and so much hotter than the 45º everyone knows, here is a sweet 60º line pattern.
Source Atle Mo
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
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