From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Derived from an image that was uploaded to Pixabay by TheDigitalArtist
Source Firkin
From a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Zero CC tileable seed texture, edited by me to be seamless from a Pixabay image. CC0
Source Sojan Janso
You don’t see many mid-tone patterns here, but this one is nice.
Source Joel Klein
I guess this one is inspired by an office. A dark office.
Source Andrés Rigo.
Fabric-ish patterns are close to my heart. French Stucco to the rescue.
Source Christopher Buecheler
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
Derived from a drawing in 'The Murmur of the Shells', Samuel Cowen, 1879.
Source Firkin
A background pattern inspired by designs seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
Super detailed 16×16 tile that forms a beautiful pattern of straws.
Source Pavel
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Classic vertical lines, in all its subtlety.
Source Cody L
And some more testing, this time with Seamless Studio. It’s Robots FFS!
Source Seamless Studio
A seamless green background texture. The image is distributed under a Creative Commons License (like all of the images here).
Source V. Hartikainen
A set of paper filters. The base texture is generated the same way, only the compositing mode is varied.
Source Lazur URH
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
If you like it a bit trippy, this wave pattern might be for you.
Source Ian Soper
A seamless pattern the starting point for which was a 'colour modulo' texture in Paint.net.
Source Firkin
There are many carbon patterns, but this one is tiny.
Source Designova
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight