Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
A dark striped seamless pattern suitable for use as a background on websites.
Source V. Hartikainen
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Seamless Prismatic Quadrilateral Line Art Pattern No Background
Source GDJ
Alternative colour scheme. 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
One can never have too few rice paper patterns, so here is one more.
Source Atle Mo
Brushed aluminum, in a bright gray version. Lovely 2X as well.
Source Andre Schouten
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
An interesting dark spotted pattern at an angle.
Source Hendrik Lammers
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
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
This was formed by distorting an image of a background on Pixabay.
Source Firkin
Here's a repeatable texture that resembles a light green concrete wall or something similar.
Source V. Hartikainen
No idea what Nistri means, but it’s a crisp little pattern nonetheless.
Source Markus Reiter
Utilising some flowers from Almeidah. To get the unit tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Number five from the same submitter, makes my job easy.
Source Dima Shiper
Could be paper, could be a Polaroid frame – up to you!
Source Chaos
A free light orange brown wallpaper with vertical stripes designed for use as a tiled background on websites. An yet another background pattern with vertical stripes.
Source V. Hartikainen
Derived from an image that was uploaded to Pixabay by Kaz
Source Firkin
A green background pattern with warped vertical stripes and a grunge look.
Source V. Hartikainen
Here's a subtle marble-like background for use on websites.
Source V. Hartikainen
Bigger is better, right? So here you have some large carbon fiber.
Source Factorio.us Collective
Zero CC Mossy stone tileable texture, photographed and made by me. CC0
Source Sojan Janso