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
This background pattern looks like bamboo to me. Feel free to download it for your website (for your blog perhaps?).
Source V. Hartikainen
As far as fabric patterns goes, this is quite crisp.
Source Heliodor Jalba
A heavy dark gray base, some subtle noise and a 45-degree grid makes this look like a pattern with a tactile feel to it.
Source Atle Mo
Dead simple but beautiful horizontal line pattern.
Source Fabian Schultz
You guessed it – looks a bit like cloth.
Source Peax Webdesign
From a drawing in 'Az Osztrák-Magyar Monarchia irásban és képben', 1885.
Source Firkin
A repeating background with wood/straw like texture.
Source V. Hartikainen
Colour version of the original pattern inspired by the front cover of 'Old and New Paris', Henry Edwards, 1894.
Source Firkin
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
This is a semi-dark pattern, sort of linen-y.
Source Sagive SEO
Prismatic Abstract Background Design No Black
Source GDJ
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I. Version with black background.
Source Firkin
A beautiful dark padded pattern, like an old classic sofa.
Source Chris Baldie
Bigger is better, right? So here you have some large carbon fiber.
Source Factorio.us Collective
Background Wall, Art Abstract, Block Well & CC0 texture.
Source Ractapopulous
This is the remix of "blue wave-seigaiha".The image depicts a seamless pattern of the front upper part of Japanese five yen coin which is used currently.This design represents a rice with ripe golden ears.
Source Yamachem
White circles connecting on a light gray background.
Source Mark Collins