The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
A heavy dark gray base, some subtle noise and a 45-degree grid makes this look like a pattern with a tactile feel to it.
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
A background pattern with a look of rough fabric.
Source V. Hartikainen
From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.
Source Firkin
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
As simple and subtle as it gets. But sometimes that’s just what you want.
Source Designova
Floral patterns will never go out of style, so enjoy this one.
Source Lasma
Tiny circle waves, almost like the ocean.
Source Sagive
Prismatic Polyskelion Pattern No Background
Source GDJ
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Groovy Concentric Background 4
Source GDJ
This one is amazing, truly original. Go use it!
Source Viahorizon
Not so subtle. These tileable wood patterns are very useful.
Source Elemis
A version without colours blended together to give a different look.
Source Firkin
A dark metal plate with an embossed grid pattern and a bit of rust. Here's a dark metal plate texture for use as a tiled background on web pages.
Source V. Hartikainen
Real snow that tiles, not easy. This is not perfect, but an attempt.
Source Atle Mo
Bumps, highlight and shadows – all good things.
Source Badhon Ebrahim
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Turn your site into a dragon with this great scale pattern.
Source Alex Parker