A seamless green background texture. The image is distributed under a Creative Commons License (like all of the images here).
Source V. Hartikainen
Not so subtle. These tileable wood patterns are very useful.
Source Elemis
A pattern derived from repeating unit cells each derived from part of a fractal rendering in paint.net.
Source Firkin
From a drawing in 'Storia del Palazzo Vecchio in Firenze', Aurelio Gotti, 1889.
Source Firkin
This is indeed a bit strange, but here’s to the crazy ones!
Source Christopher Buecheler
A repeatable image with dark background and metal grid pattern.
Source V. Hartikainen
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight