I took the liberty of using Dmitry’s pattern and made a version without perforation.
Source Atle Mo
Nice and simple crossed lines in dark gray tones.
Source Stefan Aleksić
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
Just like your old suit, all striped and smooth.
Source Alex Berkowitz
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury
Free tiled background with colorful stripes and white splatter.
Source V. Hartikainen
Honestly, who does not like a little pipe and mustache?
Source Luca Errico
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
Dark, crisp and subtle. Tiny black lines on top of some noise.
Source Wilmotte Bastien
Prismatic Rounded Squares Grid 4 No Background
Source GDJ
This background pattern looks like bamboo to me. Feel free to download it for your website (for your blog perhaps?).
Source V. Hartikainen
Three shades of gray makes this pattern look like a small carbon fiber surface. Great readability even for small fonts.
Source Atle Mo
A very dark asfalt pattern based off of a photo taken with my iPhone.
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 new one called white wall, not by me this time.
Source Yuji Honzawa
A browner version of the original weathered fence texture.
Source Firkin
An alternative colour scheme to the original seamless pattern.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
This background pattern contains worn out colorful stripes as a texture.
Source V. Hartikainen
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
A seamless chequerboard pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
Super simple but very nice indeed. Gray with vertical stripes.
Source Merrin Macleod