In the spirit of WWDC 2011, here is a dark iOS inspired linen pattern.
Source Atle Mo
A seamless pattern of "sewn stripes" colored in light gray.
Source V. Hartikainen
Same as the black version, but now in shades of gray. Very subtle and fine grained.
Source Atle Mo
Light gray pattern with an almost wall tile-like appearance.
Source Markus Tinner
Remixed from a drawing in 'Canadian forest industries July-December', 1915
Source Firkin
An abstract pale yellow paper-like background with stains colored in yellow and green.
Source V. Hartikainen
A seamless pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i. Derived from a design in 'Storia del Palazzo Vecchio in Firenze', Aurelio Gotti, 1889.
Source Firkin
Seamless pattern made from a tile that can be obtained in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
You just can’t get enough of the fabric patterns, so here is one more for your collection.
Source Krisp Designs
From a drawing in 'Picturesque New Guinea', J Lindt, 1887.
Source Firkin
A seamless pattern the starting point for which was a 'light rays' rendering in Paint.net.
Source Firkin
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
From a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Abstract Tiled Background Extended 12
Source GDJ
Derived from a drawing in 'Elfrica. An historical romance of the twelfth century', Charlotte Boger, 1885
Source Firkin
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Abstract Ellipses Background Grayscale
Source GDJ
It looks like a polished stone surface to me. Download it for free, as always.
Source V. Hartikainen
Alternative colour scheme. 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
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
This is sort of fresh, but still feels a bit old school.
Source Martuchox