I took the liberty of using Dmitry’s pattern and made a version without perforation.
Source Atle Mo
This one is amazing, truly original. Go use it!
Source Viahorizon
From a drawing in 'La Principauté de Liège et les Pays-Bas au XVIe siècle', Société des Bibliophiles Liégeois ,1887.
Source Firkin
Prismatic Groovy Concentric Background No Black
Source GDJ
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Looks a bit like concrete with subtle specks spread around the pattern.
Source Mladjan Antic
Formed by distorting a JPG from PublicDomainPictures
Source Firkin
White circles connecting on a light gray background.
Source Mark Collins
Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury
A background pattern with a look of rough fabric.
Source V. Hartikainen
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
You may use it as is, or modify it as you like.
Source V. Hartikainen