Not so subtle. These tileable wood patterns are very useful.
Source Elemis
Three shades of gray makes this pattern look like a small carbon fiber surface. Great readability even for small fonts.
Source Atle Mo
Background formed from the iconic plastic construction bricks that gave me endless hours of fun when I was a lad.
Source Firkin
You know you can’t get enough of these linen-fabric-y patterns.
Source James Basoo
Zero CC tileable bark texture, photographed and made by me. CC0
Source Sojan Janso
A seamless pattern recreated from an image on Pixabay. It is reminiscent of parquet flooring and is formed from a square tile, which can be recovered in Inkscape by selecting the ungrouped rectangle and using shift-alt-I together.
Source Firkin
Background pattern made in "Grunge-Like" style. Available in both SVG and JPG formats. Edit to your needs then click the download button.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Here's an yet another seamless note paper texture for use as a background on websites.
Source V. Hartikainen
Not a flat you live inside, like in the UK – but a flat piece of cardboard.
Source Appleshadow
This is a semi-dark pattern, sort of linen-y.
Source Sagive SEO
A repeating background with dark brown stone-like texture and abstract pattern that looks like tree trunks.
Source V. Hartikainen
Remixed from a PNG that was uploaded to Pixabay by gingertea
Source Firkin
From a drawing in 'Gately's World's Progress', Charles Beale, 1886.
Source Firkin
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin
It looks like a polished stone surface to me. Download it for free, as always.
Source V. Hartikainen
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
More tactile goodness. This time in the form of some rough cloth.
Source Bartosz Kaszubowski