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
Sharp pixel pattern, just like the good old days.
Source Paridhi
With a name this awesome, how can I go wrong?
Source Nikolay Boltachev
Bigger is better, right? So here you have some large carbon fiber.
Source Factorio.us Collective
A seamless background pattern of dark brown wood planks.
Source V. Hartikainen
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
Source Firkin
Remixed from a JPG that was uploaded to Pixabay by susanlu4esm
Source Firkin
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
You guessed it – looks a bit like cloth.
Source Peax Webdesign
Like the name says, light and gray, with some small dots and circles.
Source Brenda Lay
This could be a hippy vintage wallpaper.
Source Tileable Patterns
A pattern formed from a squared tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Zero CC tileable dry grass texture, photographed and made by me. CC0
Source Sojan Janso
Zero CC tillable hard cover red book with X shape marks. Scanned and made by me.
Source Sojan Janso
After 1 comes 2, same but different. You get the idea.
Source Hendrik Lammers
A repeating background of thick textured paper. Actually, it turned out to look like something between a paper and fabric.
Source V. Hartikainen
Here's a new background image for websites with a seamless pink texture. It should look beautiful with website themes where light pink background is needed. The background is seamless, therefore it should be used as a tiled background.
Source V. Hartikainen
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Prismatic Curved Diamond Pattern 7 No Background
Source GDJ
This is so subtle I hope you can see it! Tweak at will.
Source Alexandre Naud
Nasty or not, it’s a nice pattern that tiles. Like they all do.
Source Badhon Ebrahim