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
From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.
Source Firkin
Here's a camo print with more tan and less green, such as might be used in a desert scenario. This is tileable, so it can be used as a wallpaper or background.
Source Eady
Another fairly simple design drawn in Paint.net and vectorized in Inkscape.
Source Firkin
A heavy dark gray base, some subtle noise and a 45-degree grid makes this look like a pattern with a tactile feel to it.
Source Atle Mo
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
A large pattern with funky shapes and form. An original. Sort of origami-ish.
Source Luuk van Baars
Simple gray checkered lines, in light tones.
Source Radosław Rzepecki
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A seamlessly repeating background pattern of wood. The image is procedurally generated, and, I think, it's turned out quite well.
Source V. Hartikainen
Hey, you never know when you’ll need a bird pattern, right?
Source Pete Fecteau
Seamless Prismatic Pythagorean Line Art Pattern No Background. A seamless pattern that includes the original tile (go to Objects / Pattern / Pattern To Objects in Inkscape's menu to extract it).
Source GDJ