Not so subtle. These tileable wood patterns are very useful.
Source Elemis
The classic 45-degree diagonal line pattern, done right.
Source Jorick van Hees
A seamless pattern the starting point for which was a 'light rays' rendering in Paint.net.
Source Firkin
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin
Dark and hard, just the way we like it. Embossed triangles makes a nice pattern.
Source Ivan Ginev
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
From a drawing in 'Cassell's Library of English Literature', Henry Morley, 1883.
Source Firkin
One more updated pattern. Not really carbon fiber, but it’s the most popular pattern, so I’ll give you an extra choice.
Source Atle Mo
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
People seem to enjoy dark patterns, so here is one with some circles.
Source Atle Mo
This ladies and gentlemen, is texturetastic! Love it.
Source Adam Pickering
The image depicts a seamless pattern of a snow crystal.I referred to a book called ”sekka-zusetsu” or "雪華図説" which means an illustrated explanation about snow crystals.This book was published in 1832 (天保3年) or Edo period.For more about "雪華図説",see here:dl.ndl.go.jp/info:ndljp/pid/2536975
Source Yamachem
From a drawing in 'Prose and Verse ', William Linton, 1836.
Source Firkin
Not the most creative name, but it’s a good all-purpose light background.
Source Dmitry
You don’t see many mid-tone patterns here, but this one is nice.
Source Joel Klein
Prismatic Hexagonalism Pattern No Background
Source GDJ
Remixed from an image on Pixabay uploaded by Prawny
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
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
Prismatic Geometric Tessellation Pattern 3 No Background
Source GDJ
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
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
One more brick pattern. A bit more depth to this one.
Source Benjamin Ward