An abstract texture of water. It's not perfect, but will do. You may download if you like it.
Source V. Hartikainen
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
Prismatic Geometric Pattern Background
Source GDJ
Prismatic Snowflakes Pattern 2 No Background
Source GDJ
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Fake or not, it’s quite luxurious.
Source Factorio.us Collective
A playful triangle pattern with different shades of gray.
Source Dimitrie Hoekstra
Classic 45-degree pattern, light version.
Source Luke McDonald
Coming in at 666x666px, this is an evil big pattern, but nice and soft at the same time.
Source Atle Mo
Not sure if this is related to the Nami you get in Google image search, but hey, it’s nice!
Source Dertig Media
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Here's a new paper-like background for free use on personal and commercial projects (this applies to all background patterns here).
Source V. Hartikainen
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
Alternative colour scheme to the original.
Source Firkin
Geometric lines are always hot, and this pattern is no exception.
Source Listvetra
A seamless pattern drawn originally in Paint.net by distorting a slice of background pattern 116 and copying the resulting triangle numerous times.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Looks a bit like concrete with subtle specks spread around the pattern.
Source Mladjan Antic
Same as the black version, but now in shades of gray. Very subtle and fine grained.
Source Atle Mo
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Not even 1kb, but very stylish. Gray thin lines.
Source Struck Axiom
Just like your old suit, all striped and smooth.
Source Alex Berkowitz
This background pattern contains a seamless texture of bark. It's not very realistic, but I think it looks quite nice.
Source V. Hartikainen
Honestly, who does not like a little pipe and mustache?
Source Luca Errico
Remixed from a raster on Pixabay that was uploaded by ArtsyBee.
Source Firkin
Light gray grunge wall with a nice texture overlay.
Source Adam Anlauf