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
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
Number 2 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
This one is so simple, yet so good. And you know it. Has to be in the collection.
Source Gluszczenko
This one is super crisp at 2X. Lined paper with some dust and scratches.
Source HQvectors
To get the tile this is made up from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A nice and simple gray stucco material. Great on its own, or as a base for a new pattern.
Source Bartosz Kaszubowski
A seamless background pattern with impressed gray dots.
Source V. Hartikainen
Light gray grunge wall with a nice texture overlay.
Source Adam Anlauf
Brushed aluminum, in a bright gray version. Lovely 2X as well.
Source Andre Schouten
Sort of reminds me of those old house wallpapers.
Source Tish
Same classic 45-degree pattern, dark version.
Source Luke McDonald
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Psychedelic Geometric Background No Black
Source GDJ
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
A simple but elegant classic. Every collection needs one of these.
Source Christopher Burton
Remixed from a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
Seamless Background For Websites. It has a texture similar to cork-board.
Source V. Hartikainen
A repeatable image with dark background and metal grid pattern.
Source V. Hartikainen
A blue gray fabric-like texture for websites. An yet another fabric-like texture. It has subtle vertical and diagonal stripes to it.
Source V. Hartikainen