Remixed from a design on Pixabay. To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Scanned some rice paper and tiled it up for you. Enjoy.
Source Atle Mo
It’s okay to be square! A nice light gray pattern with random squares.
Source Waseem Dahman
Number five from the same submitter, makes my job easy.
Source Dima Shiper
A brown seamless wood texture in a form of stripe pattern. The result has turned out pretty well, in my opinion.
Source V. Hartikainen
ZeroCC tileable mossy (lichen) stone texture, edited from pixabay. CC0
Source Sojan Janso
From a drawing in 'Az Osztrák-Magyar Monarchia irásban és képben', 1885.
Source Firkin
This is so subtle you need to bring your magnifier!
Source Carlos Valdez
Light gray paper pattern with small traces of fiber and some dust.
Source Atle Mo
Floral patterns will never go out of style, so enjoy this one.
Source Lasma
From a drawing in 'In an Enchanted Island', William Mallock, 1892.
Source Firkin
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
Prismatic Groovy Concentric Background 3
Source GDJ
Oh yes, it happened! A pattern in full color.
Source Atle Mo
Paper pattern with small dust particles and 45-degree strokes.
Source Atle Mo
Remixed from a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Remixed from a design seen on Pixabay. The basic tile can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Prismatic Groovy Concentric Background 2 No Black
Source GDJ