I took the liberty of using Dmitry’s pattern and made a version without perforation.
Source Atle Mo
Inspired by this, I came up with this pattern. Madness!
Source Atle Mo
This one needs to be used in small areas; you can see it repeat.
Source Luca
Formed from a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
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
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Prismatic Groovy Concentric Background 3
Source GDJ
From a design found in 'History of the Virginia Company of London; with letters to and from the first Colony, never before printed', Edward Neill, 1869.
Source Firkin
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
Source Firkin
This seamless light brown background texture resembles a wallpaper with vertical stripes. One way to use it is as a tiled background on web sites.
Source V. Hartikainen
Basket Fibers, Basket Texture, Braid Background style CC0 texture.
Source 1A-Photoshop
Light and tiny, just the way you like it.
Source Rohit Arun Rao
Scanned some rice paper and tiled it up for you. Enjoy.
Source Atle Mo
Here's a subtle marble-like background for use on websites.
Source V. Hartikainen
Snap! It’s a pattern, and it’s not grayscale! Of course you can always change the color in Photoshop.
Source Atle Mo
Bumps, highlight and shadows – all good things.
Source Badhon Ebrahim
Someone was asking about how to achieve a fur pattern at #inkscape irc so tried to make a filter on it. Flood filled fractal noises rigged together. May someone find a good use for these.
Source Lazur URH
Continuing the geometric trend, here is one more.
Source Mike Warner
A seamless background of warped stripes on paper.
Source V. Hartikainen
One of the few full-color patterns here, but this one was just too good to pass up.
Source Alexey Usoltsev
Dark Tile-able Grunge Texture. I think this texture can be classified as grunge. It's free and seamless, as always.
Source V. Hartikainen
Washi (和紙?) is a type of paper made in Japan. Here’s the pattern for you!
Source Carolynne
Tiny circle waves, almost like the ocean.
Source Sagive
Derived from an image that was uploaded to Pixabay by mdmelo.
Source Firkin