Here I have tried to create something that would look like maple wood. Not sure how well it's turned out, but at least it looks like wood.
Source V. Hartikainen
A free background image with a seamless texture of cardboard. This texture of cardboard looks quite realistic, especially when is actually tiled.
Source V. Hartikainen
Continuing the geometric trend, here is one more.
Source Mike Warner
Non-seamless pattern drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Nice and simple crossed lines in dark gray tones.
Source Stefan Aleksić
A slightly more textured pattern, medium gray. A bit like a potato sack?
Source Bilal Ketab
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
From a drawing in 'Prose and Verse ', William Linton, 1836.
Source Firkin
Prismatic Geometric Pattern Background No Black
Source GDJ
Not the most creative name, but it’s a good all-purpose light background.
Source Dmitry
Pattern #100! A black classic knit-looking pattern.
Source Factorio.us Collective
Pixel by pixel, sharp and clean. Very light pattern with clear lines.
Source M.Ashok
Fix side and a seamless pattern formed from circles.
Source SliverKnight
A pattern formed from a squared tile. The tile can be accessed in Inkscape by selecting the rectangle 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
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
On a large canvas you can see it tiling, but used on smaller areas, it’s beautiful.
Source Paul Phönixweiß