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
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Prismatic Abstract Line Art Pattern Background 2
Source GDJ
Zero CC tileable dry grass texture, photographed and made by me. CC0
Source Sojan Janso
There are many carbon patterns, but this one is tiny.
Source Designova
A simple but elegant classic. Every collection needs one of these.
Source Christopher Burton
A free seamless background pattern for use on websites.
Source V. Hartikainen
Seamless Light Background Texture.
Source V. Hartikainen
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
A pattern formed from a squared tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
A subtle shadowed checkered pattern. Increase the lightness for even more subtle sexiness.
Source Josh Green
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Here's an yet another background for websites, with a seamless texture of wood planks this time.
Source V. Hartikainen
A seamless pattern formed from a square tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Groovy Concentric Background 3
Source GDJ
Prismatic Polka Dots Mark II 2 No Background
Source GDJ
Detailed but still subtle and quite original. Lovely gray shades.
Source Kim Ruddock
The perfect pattern for all your blogs about type, or type-related matters.
Source Atle Mo
Prismatic Geometric Pattern Background No Black
Source GDJ
Background pattern originally a PNG drawn in Paint.net
Source Firkin