A smooth mid-tone gray, or low contrast if you will, linen pattern.
Source Jordan Pittman
A simple example on using clones. You can generate a nice base for a pattern fill quickly with it.
Source Lazur URH
Another fairly simple design drawn in Paint.net and vectorized in Inkscape.
Source Firkin
Embossed lines and squares with subtle highlights.
Source Alex Parker
A bit like smudged paint or some sort of steel, here is scribble light.
Source Tegan Male
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i
Source Firkin
Number 5 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
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
Remixed from a drawing in 'Incidents on a Journey through Nubia to Darfoor', F. Ensor, 1891.
Source Firkin
A seamless pattern with green and yellow diagonal lines on top of a white dotted background.
Source V. Hartikainen
Like the name says, light and gray, with some small dots and circles.
Source Brenda Lay
This background pattern contains a seamless texture of bark. It's not very realistic, but I think it looks quite nice.
Source V. Hartikainen
Prismatic Geometric Tessellation Pattern No Background
Source GDJ
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
Source Firkin
Remixed from a drawing in 'Works. Popular edition', John Ruskin, 1886.
Source Firkin
Just what the name says, paper fibers. Always good to have.
Source Heliodor jalba
CC0 remixed from a drawing. Walter Crane, 1914, Firkin.
Source SliverKnight
The image is a seamless pattern of a fishnet.
Source Yamachem
Colorful Floral Background 3 No Black
Source GDJ
Medium gray pattern with small strokes to give a weave effect.
Source Catherine
Prismatic Groovy Concentric Background No Black
Source GDJ
Derived from a drawing in 'Historiske Afhandlinger', Adolf Jorgensen, 1898.
Source Firkin
Prismatic Chevrons Pattern 5 With Background
Source GDJ
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A seamless pattern based on a square tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin