Zero CC bark from fur tree tileable texture, photographed and made by me. CC0
Source Sojan Janso
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Bright gray tones with a hint of some metal surface.
Source Hendrik Lammers
Sharp pixel pattern looking like some sort of fabric.
Source Dmitry
Don’t look at this one too long if you’re high on something.
Source Luuk van Baars
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Prismatic Curved Diamond Pattern 2 No Background
Source GDJ
Some more diagonal lines and noise, because you know you want it.
Source Atle Mo
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
This one is quite simple in design, it consists of vertical stripes layered on top of a seamless texture.
Source V. Hartikainen
The tile can be had by selecting the rectangle in Inkscape and using shift+alt+i. Remixed from a drawing in 'Flowers of Song', Frederick Weatherly, 1895.
Source Firkin
Subtle scratches on a light gray background.
Source Andrey Ovcharov
A seamless pattern formed from a square tile based on a jpg on Pixabay. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I.
Source Firkin
A black tile-able background with paper-like texture.
Source V. Hartikainen
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Background formed from the original with an emboss effect
Source GDJ
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Prismatic Geometric Pattern Background 2 No Black
Source GDJ
Like the name suggests, this background image consists of a pattern of dark bricks. It may be an option for you, if you are looking for something that looks like a brick wall for use as a background on web pages. It's not a masterpiece, but looks pretty nice when is tiled.
Source V. Hartikainen
Abstract Geometric Monochrome Pattern Prismatic No Background
Source GDJ
Prismatic Curved Diamond Pattern 6 No Background
Source GDJ
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
Derived from a PNG that was uploaded to Pixabay by nutkitten
Source Firkin
Background Wall, Art Abstract, white Well & CC0 texture.
Source Ractapopulous