In the spirit of WWDC 2011, here is a dark iOS inspired linen pattern.
Source Atle Mo
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
Semi-light fabric pattern made out of random pixels in shades of gray.
Source Atle Mo
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Bright gray tones with a hint of some metal surface.
Source Hendrik Lammers
Abstract Tiled Background Extended 10
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. A version of the original with random colors.
Source Firkin
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
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
Classy golf-pants pattern, or crossed stripes if you will.
Source Will Monson
A free tileable background colored in off-white (antique white) color.
Source V. Hartikainen
A seamless gray background texture suitable for use on websites. To me, it has the look of stone. Feel free to modify it to meet your needs (by making it a bit lighter or darker, for example).
Source V. Hartikainen
Prismatic Groovy Concentric Background
Source GDJ
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Prismatic Floral Pattern 3 Variation 3 No Background
Source GDJ
Tiny, tiny 3D cubes. Reminds me of the good old pattern from k10k.
Source Etienne Rallion
From a drawing in 'Artists and Arabs', Henry Blackburn, 1868
Source Firkin
Prismatic Groovy Concentric Background 3 No Black
Source GDJ
ZeroCC tileable mossy (lichen) stone texture, edited from pixabay. CC0
Source Sojan Janso
A seamless dark leather-like background texture with diagonal lines that look like stitches.
Source V. Hartikainen
Prismatic Polka Dots 3 No Background
Source GDJ