I guess this is inspired by the city of Ravenna in Italy and its stone walls.
Source Sentel
Dark, square, clean and tidy. What more can you ask for?
Source Jaromír Kavan
This is indeed a bit strange, but here’s to the crazy ones!
Source Christopher Buecheler
Snap! It’s a pattern, and it’s not grayscale! Of course you can always change the color in Photoshop.
Source Atle Mo
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
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
The classic notebook paper with horizontal stripes.
Source Are Sundnes
Prismatic Triangular Background Design Mark II 5
Source GDJ
A seamless pattern based on a rectangular tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Here I have tried to create something that would look like maple wood. Not sure how well it's turned out, but at least it looks like wood.
Source V. Hartikainen
More Japanese-inspired patterns, Gold Scales this time.
Source Josh Green
White little knobs, coming in at 10x10px. Sweet!
Source Amos
Prismatic Abstract Line Art Pattern Background 2
Source GDJ
A free seamless background image with a texture of dark red "canvas". It should look very nice on web sites.
Source V. Hartikainen
Classic 45-degree pattern, light version.
Source Luke McDonald
A seamless pattern formed from cross 4. To get the original tile select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
First pattern tailor-made for Retina, with many more to come. All the old ones are upscaled, in case you want to re-download.
Source Atle Mo
Derived from a PNG that was uploaded to Pixabay by nutkitten
Source Firkin
A white version of the very popular linen pattern.
Source Ant Ekşiler
You just can’t get enough of the fabric patterns, so here is one more for your collection.
Source Krisp Designs
Pixel by pixel, sharp and clean. Very light pattern with clear lines.
Source M.Ashok
Prismatic Geometric Pattern Variation 2 With Background
Source GDJ
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin