Uses spirals from Pixabay. To get the basic tile select the rectangle in Inkscape and use shift+alt+i
Source Firkin
Because I love dark patterns, here is Brushed Alum in a dark coating.
Source Tim Ward
ZeroCC tileable stone texture, edited from pixabay. CC0
Source Sojan Janso
No, not the band but the pattern. Simple squares in gray tones, of course.
Source Atle Mo
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Prismatic Hypnotic Pattern No Background
Source GDJ
A seamless chequerboard pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i. Alternative colour scheme.
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 3
Source GDJ
Remixed from a raster on Pixabay that was uploaded by ArtsyBee.
Source Firkin
Prismatic Groovy Concentric Background 3
Source GDJ
Sharp pixel pattern, just like the good old days.
Source Paridhi
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
From a drawing in 'Gately's World's Progress', Charles Beale, 1886.
Source Firkin