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
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
Inspired by a drawing in 'Kulturgeschichte', Freidrich Hellwald, 1896.
Source Firkin
This texture looks like old leather. It should look great as a background on web pages.
Source V. Hartikainen
It’s a hole, in a pattern. On your website. Dig it!
Source Josh Green
Inspired by a JPG that was uploaded to Pixabay by kokon_art
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
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Same as gray sand but lighter. A sandy pattern with small light dots, and some angled strokes.
Source Atle Mo
Thin lines, noise and texture creates this crisp dark denim pattern.
Source Marco Slooten
This reminds me of Game Cube. A nice light 3D cube pattern.
Source Sander Ottens
A topographic map like this has actually been requested a few times, so here you go!
Source Sam Feyaerts
Abstract Tiled Background Extended 8
Source GDJ
A slightly grainy paper pattern with small horizontal and vertical strokes.
Source Atle Mo
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
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
Here's a quite bright pink background pattern for use on websites. It doesn't look like a real fur, but it definitely resembles one.
Source V. Hartikainen
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Sharp pixel pattern looking like some sort of fabric.
Source Dmitry
One can never have too few rice paper patterns, so here is one more.
Source Atle Mo
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Retro Circles Background 8 No Black
Source GDJ
Background Wall, Art Abstract, Blue Well & CC0 texture.
Source Ractapopulous