A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
Source Firkin
Inspired by a design found in 'Konstantinápolyi emlékeim', Miklos Chriszto, 1893.
Source Firkin
This texture looks like old leather. It should look great as a background on web pages.
Source V. Hartikainen
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Never out of fashion and so much hotter than the 45º everyone knows, here is a sweet 60º line pattern.
Source Atle Mo
A seamless paper background colored in pale yellow.
Source V. Hartikainen
Nicely crafted paper pattern, although a bit on the large side (500x593px).
Source Blaq Annabiosis
Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Dark, lines, noise, tactile. You get the drift.
Source Anatoli Nicolae
Zero CC tileable bark texture, photographed and made by me. CC0
Source Sojan Janso
Like the name suggests, this background image consists of a pattern of dark bricks. It may be an option for you, if you are looking for something that looks like a brick wall for use as a background on web pages. It's not a masterpiece, but looks pretty nice when is tiled.
Source V. Hartikainen
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
Remixed from a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
One more sharp little tile for you. Subtle circles this time.
Source Blunia
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Zero CC tileable Laminate wood texture, photographed and made by me. CC0
Source Sojan Janso
In the spirit of WWDC 2011, here is a dark iOS inspired linen pattern.
Source Atle Mo
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Actually, there's no clouds in it, but I think it looks quite nice.
Source V. Hartikainen