A seamless dark leather-like background texture with diagonal lines that look like stitches.
Source V. Hartikainen
A very dark spotted twinkle pattern for your twinkle needs.
Source Badhon Ebrahim
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
This light blue background pattern is quite pleasing to the eye, it consists of a tiny rough grid pattern, which is seamless by design. That's it, if you like the color, you can use this seamless pattern in a web design without making any further modifications to it.
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
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Might not be super subtle, but quite original in its form.
Source Alex Smith
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
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Looks as if it's spray painted on the wall. You can be sure that this pattern will seamlessly fill your backgrounds on web pages.
Source V. Hartikainen
From a design found in 'History of the Virginia Company of London; with letters to and from the first Colony, never before printed', Edward Neill, 1869.
Source Firkin
Prismatic Hypnotic Pattern 2 No Background
Source GDJ