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
Non-seamless pattern drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Prismatic Geometric Pattern Variation 2 With Background
Source GDJ
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
From a drawing in 'Cowdray: the history of a great English House', Julia Roundell, 1884.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
I’m starting to think I have a concrete wall fetish.
Source Atle Mo
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Geometric Pattern Background No Black
Source GDJ
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen
From a drawing in 'A Life Interest', Mrs Alexander, 1888.
Source Firkin
Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
Here's a repeatable texture that resembles a light green concrete wall or something similar.
Source V. Hartikainen
Nothing like a clean set of bed sheets, huh?
Source Badhon Ebrahim
Abstract Stars Geometric Pattern Prismatic No Background
Source GDJ
Prismatic Groovy Concentric Background 3
Source GDJ
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
An interesting dark spotted pattern at an angle.
Source Hendrik Lammers