I know there is one here already, but this is sexy!
Source Gjermund Gustavsen
A background pattern inspired by designs seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
An abstract texture of water. It's not perfect, but will do. You may download if you like it.
Source V. Hartikainen
As simple and subtle as it gets. But sometimes that’s just what you want.
Source Designova
From an image on opengameart.org shared by rubberduck.
Source Firkin
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
This is a semi-dark pattern, sort of linen-y.
Source Sagive SEO
Seamless Prismatic Geometric Pattern With Background
Source GDJ
From a design found in 'History of the Virginia Company of London; with letters to and from the first Colony, never before printed', Edward Neill, 1869.
Source Firkin
Fix side and a seamless pattern formed from circles.
Source SliverKnight
After 1 comes 2, same but different. You get the idea.
Source Hendrik Lammers
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin