Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
Nice and simple crossed lines in dark gray tones.
Source Stefan Aleksić
Zero CC tileable hard cover red book, scanned and made by me. CC0
Source Sojan Janso
Remixed from an image on Pixabay, the original having been uploaded by darkmoon1968.
Source Firkin
Light honeycomb pattern made up of the classic hexagon shape.
Source Federica Pelzel
Gold Triangular Seamless Pattern No Background
Source GDJ
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
A seamless canvas texture for using as background on websites. Colored in pale tones of brown.
Source V. Hartikainen
A seamless pattern the starting point for which was a 'rainbow twist' texture in Paint.net.
Source Firkin
A free black metallic background pattern. Here's a new pattern I made that looks metallic.
Source V. Hartikainen
From a drawing in 'Hundert Jahre in Wort und Bild', S. Stefan, 1899.
Source Firkin
Another fairly simple design drawn in Paint.net and vectorized in Inkscape.
Source Firkin
This background pattern looks like bamboo to me. Feel free to download it for your website (for your blog perhaps?).
Source V. Hartikainen
Derived from a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Vertical lines with a bumpy, yet crisp, feel to it.
Source Raasa
Use shift+alt+i on the selected rectangle in Inkscape to get the tile this is based on
Source Firkin
This is a semi-dark pattern, sort of linen-y.
Source Sagive SEO
Hey, you never know when you’ll need a bird pattern, right?
Source Pete Fecteau
Remixed from a drawing in 'The Canadian horticulturist', 1892
Source Firkin
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin