Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
From a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
Simple gray checkered lines, in light tones.
Source Radosław Rzepecki
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
The file was named striped lens, but hey – Translucent Fibres works too.
Source Angelica
Retro Circles Background 4 No Black
Source GDJ
A seamless pattern drawn originally in Paint.net by distorting a slice of background pattern 116 and copying the resulting triangle numerous times.
Source Firkin
Adapted heavily from a JPG that was uploaded to Pixabay by Viscious-Speed.
Source Firkin
A playful triangle pattern with different shades of gray.
Source Dimitrie Hoekstra
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A seamless pattern created from a square tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
White circles connecting on a light gray background.
Source Mark Collins
This is sort of fresh, but still feels a bit old school.
Source Martuchox
A seamless pattern the starting point for which was a 'rainbow twist' texture in Paint.net.
Source Firkin
A mid-tone gray pattern with some cement looking texture.
Source Hendrik Lammers
A seamless background tile of aged paper with shabby look.
Source V. Hartikainen
From a drawing in 'Artists and Arabs', Henry Blackburn, 1868.
Source Firkin
Black brick wall pattern. Brick your site up!
Source Alex Parker
Alternative colour scheme. Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Prismatic Polka Dots Mark II 3 No Background
Source GDJ
Plywood Web Background background image for use in web design.
Source V. Hartikainen