Here's a repeatable texture that resembles a light green concrete wall or something similar.
Source V. Hartikainen
The basic shapes never get old. Simple triangle pattern.
Source Atle Mo
Colour version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
A brown metallic grid pattern layered on top of a dark fabric texture. It should look great when using as a tiled background on web pages, especially blogs.
Source V. Hartikainen
Prismatic Groovy Concentric Background 4 No Black
Source GDJ
Simple combination of stripy squares with their negatively coloured counterparts
Source Firkin
From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.
Source Firkin
Remixed from a JPG that was uploaded to Pixabay by susanlu4esm
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
No relation to the band, but damn it’s subtle!
Source Thomas Myrman
ZeroCC tileable beechwood wood texture, generated in Neo Texture Edit by me. CC0
Source Sojan Janso
From a drawing in 'Resa i Afrika, genom Angola, Ovampo och Damaraland', P. Moller, 1899.
Source Firkin
Light and tiny, just the way you like it.
Source Rohit Arun Rao
A repeating graphic with ancient pattern. I came up with this name/title at last minute, so you may find that there is very little of ancientness in this pattern after all.
Source V. Hartikainen
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin