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
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
Medium gray fabric pattern with 45-degree lines going across.
Source Atle Mo
A seamless pattern formed from a square tile based on a jpg on Pixabay. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I.
Source Firkin
In the spirit of WWDC 2011, here is a dark iOS inspired linen pattern.
Source Atle Mo
Adapted from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
From drawing in 'Musings in Maoriland', Thomas Bracken, 1890.
Source Firkin
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Adapted heavily from a JPG that was uploaded to Pixabay by Viscious-Speed.
Source Firkin
A textured orange background pattern with vertical stripes.
Source V. Hartikainen
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Hexagonalist Pattern No Background
Source GDJ
A seamless pattern formed from cross 4. To get the original tile select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Fake or not, it’s quite luxurious.
Source Factorio.us Collective
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A repeating background with wood/straw like texture.
Source V. Hartikainen
Derived from a corner decoration itself found as a jpg on Pixabay.
Source Firkin
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
One of the few full-color patterns here, but this one was just too good to pass up.
Source Alexey Usoltsev