I took the liberty of using Dmitry’s pattern and made a version without perforation.
Source Atle Mo
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Washi (和紙?) is a type of paper made in Japan. Here’s the pattern for you!
Source Carolynne
Nicely crafted paper pattern, although a bit on the large side (500x593px).
Source Blaq Annabiosis
U.S.-based National Fire Protection Association standard fire diamond for flagging risks posed by hazardous materials. The red diamond has a number 0-4 depending on flammability. The blue diamond has a number 0-4 depending on health hazard. The yellow has a number 0-4 depending on reactivity. the white square has a special notice, e.g OX for oxidizer.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Embossed lines and squares with subtle highlights.
Source Alex Parker
Never out of fashion and so much hotter than the 45º everyone knows, here is a sweet 60º line pattern.
Source Atle Mo
Remixed from a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
Very dark pattern with some noise and 45-degree lines.
Source Stefan Aleksić
Little x’es, noise and all the stuff you like. Dark like a Monday, with a hint of blue.
Source Tom McArdle
Based on several public domain drawings on Wikimedia Commons. This was formed from a rectangular tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i
Source Firkin
More tactile goodness. This time in the form of some rough cloth.
Source Bartosz Kaszubowski
This one needs to be used in small areas; you can see it repeat.
Source Luca
Seamless Prismatic Pythagorean Line Art Pattern No Background. A seamless pattern that includes the original tile (go to Objects / Pattern / Pattern To Objects in Inkscape's menu to extract it).
Source GDJ
A seamless pattern the starting point for which was a 'light rays' rendering in Paint.net.
Source Firkin
A bit of scratched up grayness. Always good.
Source Dmitry
Little x’es, noise and all the stuff you like. Dark like a Monday, with a hint of blue.
Source Tom McArdle
Another fairly simple design drawn in Paint.net and vectorized in Inkscape.
Source Firkin
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss