Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
This one needs to be used in small areas; you can see it repeat.
Source Luca
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Sharp pixel pattern, just like the good old days.
Source Paridhi
Abstract Ellipses Background Grayscale
Source GDJ
A black tile-able background with paper-like texture.
Source V. Hartikainen
More in the paper realm, this time with fibers.
Source Jorge Fuentes
Seamless tile drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
Actually remixed from a pattern on Pixabay. But then noticed a very similar one on Openclipart.org uploaded by btj51q2.
Source Firkin