Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
Formed by distorting an image on Pixabay that was uploaded by gustavorezende. To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Groovy Concentric Background 5 No Black
Source GDJ
From a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
Prepared mostly as a raster in Paint.net and vectorised.
Source Firkin
Number 3 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
A seamless background tile of aged paper with shabby look.
Source V. Hartikainen
A free seamless background image with abstract texture of green "curtain".
Source V. Hartikainen
Sharp diamond pattern. A small 24x18px tile.
Source Tom Neal
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
This seamless light brown background texture resembles a wallpaper with vertical stripes. One way to use it is as a tiled background on web sites.
Source V. Hartikainen
The tile this is based on can be retrieved by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Nasty or not, it’s a nice pattern that tiles. Like they all do.
Source Badhon Ebrahim
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury
This is so subtle: We’re talking 1% opacity. Get your squint on!
Source Atle Mo
This texture looks like old leather. It should look great as a background on web pages.
Source V. Hartikainen
One more in the line of patterns inspired by Japanese/Asian styles. Smooth.
Source Kim Ruddock
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin