You know you can’t get enough of these linen-fabric-y patterns.
Source James Basoo
A dark one with geometric shapes and dotted lines.
Source Mohawk Studios
One more brick pattern. A bit more depth to this one.
Source Benjamin Ward
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
If you don’t like cream and pixels, you’re in the wrong place.
Source Mizanur Rahman
This one is super crisp at 2X. Lined paper with some dust and scratches.
Source HQvectors
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 based on a tile that can be achieved by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Sweet and subtle white plaster with hints of noise and grunge.
Source Phil Maurer
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
Prismatic Abstract Geometric Background 2 No Black
Source GDJ