Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
The classic 45-degree diagonal line pattern, done right.
Source Jorick van Hees
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
Sharp pixel pattern looking like some sort of fabric.
Source Dmitry
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
From a drawing in 'The Quiver of Love', Walter Crane, 1876
Source Firkin
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857. The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Abstract Stars Geometric Pattern Prismatic No Background
Source GDJ
This is a seamless pattern of a woody texture.The original image is here:https://pixabay.com/ja/users/ClassicallyPrinted-1302233/
Source Yamachem
A car pattern?! Can it be subtle? I say yes!
Source Radosław Rzepecki
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
This ons is quite old school looking. Retro, even. I like it.
Source Arno Declercq
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
Tiny, tiny 3D cubes. Reminds me of the good old pattern from k10k.
Source Etienne Rallion
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight