I know there is one here already, but this is sexy!
Source Gjermund Gustavsen
ZeroCC tileable mossy (lichen) stone texture, edited from pixabay. CC0
Source Sojan Janso
Background Wall, Art Abstract, Star Well & CC0 texture.
Source Ractapopulous
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
This makes me wanna shoot some pool! Sweet green pool table pattern.
Source Caveman
Seamless pattern formed from a square tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
A free background image with a seamless texture of cardboard. This texture of cardboard looks quite realistic, especially when is actually tiled.
Source V. Hartikainen
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
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
From drawing in 'Musings in Maoriland', Thomas Bracken, 1890.
Source Firkin
An alternative colour scheme for the original background.
Source Firkin
This seamless background image should look nice on websites. It has a dark blue gray texture with vertical stripes, it tiles seamlessly and, like all of the background images here, it's free. So, if you like it, take it!
Source V. Hartikainen
Just like your old suit, all striped and smooth.
Source Alex Berkowitz
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
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
White circles connecting on a light gray background.
Source Mark Collins
You know, tiny and sharp. I’m sure you’ll find a use for it.
Source Atle Mo
Fake or not, it’s quite luxurious.
Source Factorio.us Collective
This one could be the shirt of a golf player. Angled lines in different thicknesses.
Source Olivier Pineda
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Continuing the geometric trend, here is one more.
Source Mike Warner
A free seamless background image with a texture of dark red "canvas". It should look very nice on web sites.
Source V. Hartikainen