Here's a repeatable texture that resembles a light green concrete wall or something similar.
Source V. Hartikainen
A nice one indeed, but I have a feeling we have it already? If you spot a copy, let me know on Twitter.
Source Graphiste
Cubes as far as your eyes can see. You know, because they tile.
Source Jan Meeus
Derived from elements found in a floral ornament drawing on Pixabay.
Source Firkin
A seamless pattern the starting point for which was a 'light rays' rendering in Paint.net.
Source Firkin
A seamless pattern formed from a sports car on clker.com. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
This beige background pattern resembles a concrete wall with engravings or something similar to it.
Source V. Hartikainen
A seamless green background texture. The image is distributed under a Creative Commons License (like all of the images here).
Source V. Hartikainen
Smooth Polaroid pattern with a light blue tint.
Source Daniel Beaton
Remixed from a PNG that was uploaded to Pixabay by k_jprather
Source Firkin
The edges of all the red objects line up either vertically or horizontally, but it doesn't appear so. Made from a square tile that can be got by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
White circles connecting on a light gray background.
Source Mark Collins
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Formed by heavily distorting part of a an image of a fish uploaded to Pixabay by GLady
Source Firkin
Lovely pattern with some good-looking non-random noise lines.
Source Zucx
A background tile of dark textile. Made this a long time ago and just now decided to publish it.
Source V. Hartikainen
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
An interesting dark spotted pattern at an angle.
Source Hendrik Lammers
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
Background Wall, Art Abstract, white Well & CC0 texture.
Source Ractapopulous