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
Seamless Olive Green Web Background Image
Source V. Hartikainen
Just what the name says, paper fibers. Always good to have.
Source Heliodor jalba
Geometric triangles seem to be quite hot these days.
Source Pixeden
Another fairly simple design drawn in Paint.net and vectorized in Inkscape.
Source Firkin
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
That’s what it is, a dark dot. Or sort of carbon looking.
Source Tsvetelin Nikolov
Drawn in Paint.net using the kaleidoscope plug-in and vectorised.
Source Firkin
A background pattern with a look of rough fabric.
Source V. Hartikainen
This one is amazing, truly original. Go use it!
Source Viahorizon
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
From a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Just a nice looking textured pattern with faded blue stripes. Well, that's it for today... one background a day, as usual.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Here's a camo print with more tan and less green, such as might be used in a desert scenario. This is tileable, so it can be used as a wallpaper or background.
Source Eady
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
Source Firkin
Nice little grid. Would work great as a base on top of some other patterns.
Source Arno Gregorian
Prismatic Curved Diamond Pattern 8 No Background
Source GDJ
Number five from the same submitter, makes my job easy.
Source Dima Shiper
Same as Silver Scales, but in black. Turn your site into a dragon with this great scale pattern.
Source Alex Parker
I love the movie Pineapple Express, and I’m also liking this Pineapple right here.
Source Audee Mirza
White fabric looking texture with some nice random wave features.
Source Hendrik Lammers