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
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
This light yellow background pattern consists of an irregular pattern of spots. Here's a light background pattern with yellowish tint.
Source V. Hartikainen
Prismatic Groovy Concentric Background 4
Source GDJ
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
It looks like a polished stone surface to me. Download it for free, as always.
Source V. Hartikainen
Gold Triangular Seamless Pattern No Background
Source GDJ
I love these crisp, tiny, super subtle patterns.
Source Badhon Ebrahim
The first pattern on here using opacity. Try it on a site with a colored background, or even using mixed colors.
Source Nathan Spady
Non-seamless pattern drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
Like the name says, light and gray, with some small dots and circles.
Source Brenda Lay
Derived from an image that was uploaded to Pixabay by starchim01
Source Firkin
The image is a seamless pattern of a fishnet.
Source Yamachem
Small dots with minor circles spread across to form a nice mosaic.
Source John Burks
Remixed from a design seen on Pixabay. The basic tile can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Derived from a drawing in 'Elfrica. An historical romance of the twelfth century', Charlotte Boger, 1885
Source Firkin
Feel free to download and use it, or see the rest of the dark background patterns that I have made. Anyway, I hope you will find something that you like.
Source V. Hartikainen
A seamless pattern of leopard skin. It should look nice as a background element on web pages.
Source V. Hartikainen
A very dark asfalt pattern based off of a photo taken with my iPhone.
Source Atle Mo
Sometimes you just need the simplest thing.
Source Fabricio
Kaleidoscope Prismatic Abstract No Background
Source GDJ
This one needs to be used in small areas; you can see it repeat.
Source Luca
Prismatic Polyskelion Pattern No Background
Source GDJ