A seamless green background texture. The image is distributed under a Creative Commons License (like all of the images here).
Source V. Hartikainen
ZeroCC tileable stone texture, edited from pixabay. CC0
Source Sojan Janso
Hey, you never know when you’ll need a bird pattern, right?
Source Pete Fecteau
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
Source Firkin
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin
This beige background pattern resembles a concrete wall with engravings or something similar to it.
Source V. Hartikainen
From a drawing in 'Bond Slaves. The story of a struggle.', Isabella Varley, 1893.
Source Firkin
Nice and simple crossed lines in dark gray tones.
Source Stefan Aleksić
Snap! It’s a pattern, and it’s not grayscale! Of course you can always change the color in Photoshop.
Source Atle Mo
Prismatic Curved Diamond Pattern 2 No Background
Source GDJ
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A pattern drawn in Paint.net and vectorized in Vector Magic.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Horizontal and vertical lines on a light gray background.
Source Adam Anlauf
Remixed from a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin
An emulated “transparent” background pattern, like that of all kinds of computer graphics software.
Source AdamStanislav
Remixed from a drawing in 'An Index to Deering's Nottinghamia Vetus et Nova', Rupert Chicken, 1899. The unit tile can be had by selecting the rectangle in Inkscape and using shift-alt-i
Source Firkin
From a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Love the style on this one, very fresh. Diagonal diamond pattern. Get it?
Source INS
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Retro Circles Background 7 No Black
Source GDJ
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin