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
Subtle scratches on a light gray background.
Source Andrey Ovcharov
Here's an yet another seamless note paper texture for use as a background on websites.
Source V. Hartikainen
A free background pattern with abstract green tiles.
Source V. Hartikainen
Remixed from a drawing in 'Analecta Eboracensia', Thomas Widdrington, 1897.
Source Firkin
Remixed from a design seen on Pixabay. The basic tile can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Zero CC tileable seed texture, edited by me to be seamless from a Pixabay image. CC0
Source Sojan Janso
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
The tile this is based on can be retrieved by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Prismatic Polka Dots Mark II No Background
Source GDJ
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen
It’s an egg, in the form of a pattern. This really is 2012.
Source Paul Phönixweiß
One more in the line of patterns inspired by Japanese/Asian styles. Smooth.
Source Kim Ruddock