Small gradient crosses inside 45-degree boxes, or bigger crosses if you will.
Source Wassim
A subtle shadowed checkered pattern. Increase the lightness for even more subtle sexiness.
Source Josh Green
This light yellow background pattern consists of an irregular pattern of spots. Here's a light background pattern with yellowish tint.
Source V. Hartikainen
A background pattern with wavy green vertical stripes. This one has green stripes on a white background. Download if you like it.
Source V. Hartikainen
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
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
Source Firkin
Remixed from an image that was uploaded to Pixabay by KirstenStar
Source Firkin
It’s okay to be square! A nice light gray pattern with random squares.
Source Waseem Dahman
Zero CC tileable pine bark texture, photographed and made by me. CC0
Source Sojan Janso
From a drawing in 'Heroes of North African Discovery', Nancy Meugens, 1894.
Source Firkin
Remixed from a raster on Pixabay that was uploaded by ArtsyBee.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A slightly grainy paper pattern with small horizontal and vertical strokes.
Source Atle Mo
A new take on the black linen pattern. Softer this time.
Source Atle Mo
Inspired by a pattern seen on a public domain image of a very old tile. To get the unit cell, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Prismatic Abstract Line Art Pattern Background
Source GDJ
You know you can’t get enough of these linen-fabric-y patterns.
Source James Basoo
A seamless pattern of "sewn stripes" colored in light gray.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A seamless green background texture. The image is distributed under a Creative Commons License (like all of the images here).
Source V. Hartikainen
Pattern #100! A black classic knit-looking pattern.
Source Factorio.us Collective
I skipped number 3, because it wasn’t all that great. Sorry.
Source Dima Shiper
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin