I took the liberty of using Dmitry’s pattern and made a version without perforation.
Source Atle Mo
The starting point for this was a texture drawn with the 'Radial Colors' plug-in in Paint.net.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
This is indeed a bit strange, but here’s to the crazy ones!
Source Christopher Buecheler
Bit of a strange name on this one, but still nice. Tiny gray square things.
Source Carlos Valdez
Prismatic Polka Dots Mark II 3 No Background
Source GDJ
A seamless pattern formed from miutopia mug remixes on a tablecloth.
Source Firkin
Prismatic Curved Diamond Pattern No Background
Source GDJ
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
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
A hint of orange color, and some crossed and embossed lines.
Source Adam Anlauf
This tiled background comes in red and consists of tiles that look like gemstones. It is more for blogs or social profiles, I think.
Source V. Hartikainen
With a name this awesome, how can I go wrong?
Source Nikolay Boltachev
Colourful background achieved with gradient fills.
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
The edges of all the red objects line up either vertically or horizontally, but it doesn't appear so. Made from a square tile that can be got by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Remixed from a drawing in 'The March of Loyalty', Letitia MacClintock, 1884.
Source Firkin
From a tile that 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
A seamless chequerboard pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i. Alternative colour scheme.
Source Firkin
From a drawing in 'Navigations de Alouys de Cademoste.-La Navigation du Capitaine Pierre Sintre', Alvise da ca da Mosto, 1895.
Source Firkin