8 by 8 pixels, and just what the title says.
Source pixilated
More in the paper realm, this time with fibers.
Source Jorge Fuentes
Background Wall, Art Abstract, Block Well & CC0 texture.
Source Ractapopulous
A repeating background with dark brown stone-like texture and abstract pattern that looks like tree trunks.
Source V. Hartikainen
I scanned a paper coffee cup. You know, in case you need it.
Source Atle Mo
Not the most creative name, but it’s a good all-purpose light background.
Source Dmitry
Like the name says, light and gray, with some small dots and circles.
Source Brenda Lay
Dark, square, clean and tidy. What more can you ask for?
Source Jaromír Kavan
Pattern that came out of playing with the 'slinky' plug-in for Paint.net
Source Firkin
Floral patterns might not be the hottest thing right now, but you never know when you need it!
Source Lauren
A seamless pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
This tiled background comes in red and consists of tiles that look like gemstones. It is more for blogs or social profiles, I think.
Source V. Hartikainen
One more in the line of patterns inspired by Japanese/Asian styles. Smooth.
Source Kim Ruddock
A topographic map like this has actually been requested a few times, so here you go!
Source Sam Feyaerts
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
A pattern derived from repeating unit cells each derived from part of a fractal rendering in paint.net.
Source Firkin
Number five from the same submitter, makes my job easy.
Source Dima Shiper
Looks as if it's spray painted on the wall. You can be sure that this pattern will seamlessly fill your backgrounds on web pages.
Source V. Hartikainen