This seamless background image should look nice on websites. It has a dark blue gray texture with vertical stripes, it tiles seamlessly and, like all of the background images here, it's free. So, if you like it, take it!
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Prismatic Polka Dots 3 No Background
Source GDJ
Spice up your next school project with this icon background.
Source Swetha
Seamless Prismatic Pythagorean Line Art Pattern No Background. A seamless pattern that includes the original tile (go to Objects / Pattern / Pattern To Objects in Inkscape's menu to extract it).
Source GDJ
And some more testing, this time with Seamless Studio. It’s Robots FFS!
Source Seamless Studio
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Black version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
Prismatic Abstract Line Art Pattern Background
Source GDJ
The classic subtle pattern. Sort of wall/brick looking. Or moon-looking?
Source Joel Klein
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
From a drawing in 'Gately's World's Progress', Charles Beale, 1886.
Source Firkin
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
The image depicts a seamless pattern of pine tree leaves.
Source Yamachem
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A playful triangle pattern with different shades of gray.
Source Dimitrie Hoekstra
Number five from the same submitter, makes my job easy.
Source Dima Shiper
Background Wall, Art Abstract, white Well & CC0 texture.
Source Ractapopulous
Medium gray fabric pattern with 45-degree lines going across.
Source Atle Mo
Prismatic Groovy Concentric Background 4
Source GDJ
A seamless pattern recreated from an image on Pixabay. It is reminiscent of parquet flooring and is formed from a square tile, which can be recovered in Inkscape by selecting the ungrouped rectangle and using shift-alt-I together.
Source Firkin
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen