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
Background Wall, Art Abstract, Blue Well & CC0 texture.
Source Ractapopulous
Seamless Prismatic Quadrilateral Line Art Pattern No Background
Source GDJ
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Remixed from a drawing in 'Analecta Eboracensia', Thomas Widdrington, 1897.
Source Firkin
This was formed by distorting an image of a background on Pixabay.
Source Firkin
This was formed by distorting an image of a background on Pixabay.
Source Firkin
Light gray grunge wall with a nice texture overlay.
Source Adam Anlauf
Like the name says, light and gray, with some small dots and circles.
Source Brenda Lay
Not even 1kb, but very stylish. Gray thin lines.
Source Struck Axiom
A seamless gray background texture suitable for use on websites. To me, it has the look of stone. Feel free to modify it to meet your needs (by making it a bit lighter or darker, for example).
Source V. Hartikainen
Floral patterns might not be the hottest thing right now, but you never know when you need it!
Source Lauren
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Background pattern originally a PNG drawn in Paint.net
Source Firkin
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
Derived from a drawing in 'The Murmur of the Shells', Samuel Cowen, 1879.
Source Firkin
Could be paper, could be a Polaroid frame – up to you!
Source Chaos
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen
This is the third pattern called Dark Denim, but hey, we all love them!
Source Brandon Jacoby
Used a cherry by doctormo to make this seamless pattern
Source Firkin
Number 1 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos