I skipped number 3, because it wasn’t all that great. Sorry.
Source Dima Shiper
Nice and simple crossed lines in dark gray tones.
Source Stefan Aleksić
Colored maple leaves scattered on a surface. This is tileable, so it can be used as a background or wallpaper.
Source Eady
Smooth Polaroid pattern with a light blue tint.
Source Daniel Beaton
Remixed from a raster on Pixabay that was uploaded by ArtsyBee.
Source Firkin
Abstract Geometric Monochrome Pattern Prismatic No Background
Source GDJ
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
After 1 comes 2, same but different. You get the idea.
Source Hendrik Lammers
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857. The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Here's a new background image for websites with a seamless pink texture. It should look beautiful with website themes where light pink background is needed. The background is seamless, therefore it should be used as a tiled background.
Source V. Hartikainen
Cubes as far as your eyes can see. You know, because they tile.
Source Jan Meeus
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
Background pattern originally a PNG drawn in Paint.net
Source Firkin
You could get a bit dizzy from this one, but it might come in handy.
Source Dertig Media
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Simple wide squares with a small indent. Fits all.
Source Petr Šulc.
A free seamless background texture that looks like a brown stone wall.
Source V. Hartikainen
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin
The tile can be had by selecting the rectangle in Inkscape and using shift+alt+i. Remixed from a drawing in 'Flowers of Song', Frederick Weatherly, 1895.
Source Firkin
A seamless pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin