A seamless gray background texture suitable for use on websites. To me, it has the look of stone. Feel free to modify it to meet your needs (by making it a bit lighter or darker, for example).
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
Prismatic Groovy Concentric Background
Source GDJ
Remixed from a JPG that was uploaded to Pixabay by theasad121
Source Firkin
Dark and hard, just the way we like it. Embossed triangles makes a nice pattern.
Source Ivan Ginev
A free green background pattern with a pattern of rhombuses on a seamless texture. Feel free to use it as a tiled background image on your web site.
Source V. Hartikainen
Prismatic Hexagonalist Pattern No Background
Source GDJ
Embossed lines and squares with subtle highlights.
Source Alex Parker
This one takes you back to math class. Classic mathematic board underlay.
Source Josh Green
Square design drawn in Paint.net and vectorized in Vector Magic.
Source Firkin
Semi-light fabric pattern made out of random pixels in shades of gray.
Source Atle Mo
Bright Multicolored Floral Background by Karen Arnold from PDP.
Source GDJ
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Remixed from an image that was uploaded to Pixabay by Pixeline
Source Firkin
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
Prismatic Polka Dots 3 No Background
Source GDJ
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin