Based on several public domain drawings on Wikimedia Commons. This was formed from a rectangular tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Sharp diamond pattern. A small 24x18px tile.
Source Tom Neal
This one is rather fun and playful. The 2X could be used at 1X too!
Source Welsley
Inspired by a pattern seen on a public domain image of a very old tile. To get the unit cell, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Not so subtle. These tileable wood patterns are very useful.
Source Elemis
Looks like a technical drawing board: small squares forming a nice grid.
Source We Are Pixel8
Colorful Floral Background 3 No Black
Source GDJ
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
Prismatic Abstract Geometric Background 5 No Black
Source GDJ
This tiled background comes in red and consists of tiles that look like gemstones. It is more for blogs or social profiles, I think.
Source V. Hartikainen
This background has abstract texture with some similarities to wood.
Source V. Hartikainen