There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
The edges of all the red objects line up either vertically or horizontally, but it doesn't appear so. Made from a square tile that can be got by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Lovely pattern with some good-looking non-random noise lines.
Source Zucx
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
A light gray fabric pattern with faded vertical stripes.
Source V. Hartikainen
There are many carbon patterns, but this one is tiny.
Source Designova
Colour version of the original pattern inspired by the front cover of 'Old and New Paris', Henry Edwards, 1894.
Source Firkin
A seamless pattern formed from background pattern 102
Source Firkin
Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin
Sharp but soft triangles in light shades of gray.
Source Pixeden
Background Wall, Art Abstract, Blue Well & CC0 texture.
Source Ractapopulous
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen
A version without colours blended together to give a different look.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
Sharp pixel pattern looking like some sort of fabric.
Source Dmitry
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
The classic 45-degree diagonal line pattern, done right.
Source Jorick van Hees
A dark one with geometric shapes and dotted lines.
Source Mohawk Studios
This is so subtle: We’re talking 1% opacity. Get your squint on!
Source Atle Mo