Inspired by this, I came up with this pattern. Madness!
Source Atle Mo
Derived from a JPG that was uploaded to Pixabay by ractapopulous
Source Firkin
Abstract Arbitrary Geometric Background derived from an image on Pixabay.
Source GDJ
Here's an yet another background for websites, with a seamless texture of wood planks this time.
Source V. Hartikainen
A slightly grainy paper pattern with small horizontal and vertical strokes.
Source Atle Mo
Here's a subtle marble-like background for use on websites.
Source V. Hartikainen
You guessed it – looks a bit like cloth.
Source Peax Webdesign
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Adapted from an image that was uploaded to Pixabay by Anerma.
Source Firkin
And some more testing, this time with Seamless Studio. It’s Robots FFS!
Source Seamless Studio
A rusty grunge background for websites. Feel free to use it in your site's theme.
Source V. Hartikainen
Prismatic Hypnotic Pattern 2 No Background
Source GDJ
Found on the ground in french cafe in kunming, Yunnan, china
Source Rejon
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
Zero CC bark from fur tree tileable texture, photographed and made by me. CC0
Source Sojan Janso
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
An emulated “transparent” background pattern, like that of all kinds of computer graphics software.
Source AdamStanislav