This seamless background image should look nice on websites. It has a dark blue gray texture with vertical stripes, it tiles seamlessly and, like all of the background images here, it's free. So, if you like it, take it!
Source V. Hartikainen
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
A seamless pattern with a unit cell drawn as a bitmap in Paint.net and vectorized in Vector Magic.
Source Firkin
Prismatic Abstract Geometric Background derived from an image on Pixabay.
Source GDJ
Prismatic Rounded Squares Grid 3 No Background
Source GDJ
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
Someone was asking about how to achieve a fur pattern at #inkscape irc so tried to make a filter on it. Flood filled fractal noises rigged together. May someone find a good use for these.
Source Lazur URH
Very dark pattern with some noise and 45-degree lines.
Source Stefan Aleksić
Wasn't satisfied with the original's colouring. Too much component transfer and colormatrixes yet the results are lacking a bit. So this time it is a simple black to transparent fade, making it possible remixing easily once there will be other blending modes supported as well. Probably in inkscape 0.92.
Source Lazur URH
There are many carbon patterns, but this one is tiny.
Source Designova
Here's a new gray "fabric" pattern. Use it as backgrounds for websites or for other purposes.
Source V. Hartikainen
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
Colour version of the original pattern.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I.
Source Firkin
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Sharp but soft triangles in light shades of gray.
Source Pixeden
Zero CC tileable hard cover red book, scanned and made by me. CC0
Source Sojan Janso
Remixed from a PNG that was uploaded to Pixabay by gingertea
Source Firkin
Turn your site into a dragon with this great scale pattern.
Source Alex Parker
Based on several public domain drawings on Wikimedia Commons. This was formed from a rectangular tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin