In the spirit of WWDC 2011, here is a dark iOS inspired linen pattern.
Source Atle Mo
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
More carbon fiber for your collections. This time in white or semi-dark gray.
Source Badhon Ebrahim
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Prismatic Groovy Concentric Background 4
Source GDJ
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
This metal background pattern resembles a metal plate with rivets. Solid rivets on a metal plate.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
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
Stefan is hard at work, this time with a funky pattern of squares.
Source Stefan Aleksić
Geometric triangles seem to be quite hot these days.
Source Pixeden
Remixed from an image on Pixabay uploaded by Prawny
Source Firkin
A criss-cross pattern similar to one I saw mown into a sports field.
Source Firkin
Prismatic Basic Pattern 2 No Background
Source GDJ
Prismatic Geometric Tessellation Pattern 4 No Background
Source GDJ
ZeroCC tileable stone texture, edited from pixabay, CC0
Source Sojan Janso
A nice and simple white rotated tile pattern.
Source Another One
Formed by heavily distorting part of a an image of a fish uploaded to Pixabay by GLady
Source Firkin
This seamless background image should look nice on websites. It has a dark blue gray texture with vertical stripes, it tiles seamlessly and, like all of the background images here, it's free. So, if you like it, take it!
Source V. Hartikainen
Background Wall, Art Abstract, Block Well & CC0 texture.
Source Ractapopulous