Square design drawn in Paint.net and vectorized in Vector Magic.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Prismatic Groovy Concentric Background 2 No Black
Source GDJ
Derived from a PNG that was uploaded to Pixabay by nutkitten
Source Firkin
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
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
Prismatic Curved Diamond Pattern 2 No Background
Source GDJ
Derived from a drawing in 'Historiske Afhandlinger', Adolf Jorgensen, 1898.
Source Firkin
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
From a drawing in 'A Life Interest', Mrs Alexander, 1888.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Embossed lines and squares with subtle highlights.
Source Alex Parker
One more sharp little tile for you. Subtle circles this time.
Source Blunia
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Prismatic Geometric Pattern Background
Source GDJ
You guessed it – looks a bit like cloth.
Source Peax Webdesign
This one takes you back to math class. Classic mathematic board underlay.
Source Josh Green
Vector version of a JPG that was uploaded to Pixabay by theasad121
Source Firkin
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
It’s an egg, in the form of a pattern. This really is 2012.
Source Paul Phönixweiß
Prismatic Abstract Background Design No Black
Source GDJ
ZeroCC tileable moss texture, photographed and made by me. CC0
Source Sojan Janso
A seamless background texture of old cardboard.
Source V. Hartikainen
Remixed from a drawing in 'Works. Popular edition', John Ruskin, 1886.
Source Firkin