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
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
Remixed from a design on Pixabay. To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
Dark, crisp and subtle. Tiny black lines on top of some noise.
Source Wilmotte Bastien
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
Turn your site into a dragon with this great scale pattern.
Source Alex Parker
The basic shapes never get old. Simple triangle pattern.
Source Atle Mo
Light gray grunge wall with a nice texture overlay.
Source Adam Anlauf
A car pattern?! Can it be subtle? I say yes!
Source Radosław Rzepecki
Medium gray fabric pattern with 45-degree lines going across.
Source Atle Mo
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
A light brushed aluminum pattern for your pleasure.
Source Tim Ward
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Seamless pattern formed from a square tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Prismatic Abstract Line Art Pattern Background 2
Source GDJ
Colour version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
The name alone is awesome, but so is this sweet dark pattern.
Source Federica Pelzel
This background image has seamless texture that resembles a surface of gray stone.
Source V. Hartikainen
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin