From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A light gray fabric pattern with faded vertical stripes.
Source V. Hartikainen
Prismatic Curved Diamond Pattern 8 No Background
Source GDJ
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
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
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
Pattern Background, Texture, Photoshop Structure style CC0 texture.
Source Darkmoon1968
A background pattern with a look of rough fabric.
Source V. Hartikainen
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
No, not the band but the pattern. Simple squares in gray tones, of course.
Source Atle Mo
Prismatic Groovy Concentric Background 2 No Black
Source GDJ
In the spirit of WWDC 2011, here is a dark iOS inspired linen pattern.
Source Atle Mo
ZeroCC tileable beechwood wood texture, generated in Neo Texture Edit by me. CC0
Source Sojan Janso
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
Derived from an image that was uploaded to Pixabay by Kaz
Source Firkin
Background formed from the original with an emboss effect
Source GDJ
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
Background pattern made in "Grunge-Like" style. Available in both SVG and JPG formats. Edit to your needs then click the download button.
Source V. Hartikainen
From a drawing in 'In an Enchanted Island', William Mallock, 1892.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
A large (588x375px) sand-colored pattern for your ever-growing collection. Shrink at will.
Source Alex Tapein
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight