One more updated pattern. Not really carbon fiber, but it’s the most popular pattern, so I’ll give you an extra choice.
Source Atle Mo
A light gray fabric pattern with faded vertical stripes.
Source V. Hartikainen
Use shift+alt+i on the selected rectangle in Inkscape to get the tile this is based on
Source Firkin
Prismatic Snowflakes Pattern 3 No Background
Source GDJ
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Luxurious looking pattern (for a T-shirt maybe?) with a hint of green.
Source Simon Meek
In the spirit of WWDC 2011, here is a dark iOS inspired linen pattern.
Source Atle Mo
Classy golf-pants pattern, or crossed stripes if you will.
Source Will Monson
A beautiful dark wood pattern, superbly tiled.
Source Omar Alvarado
It looks like a polished stone surface to me. Download it for free, as always.
Source V. Hartikainen
The classic notebook paper with horizontal stripes.
Source Are Sundnes
A pattern derived from repeating unit cells each derived from part of a fractal rendering in paint.net.
Source Firkin
Just like your old suit, all striped and smooth.
Source Alex Berkowitz
Background formed from the iconic plastic construction bricks that gave me endless hours of fun when I was a lad.
Source Firkin
White circles connecting on a light gray background.
Source Mark Collins
You know I love paper patterns. Here is one from Stephen. Say thank you!
Source Stephen Gilbert
Nicely crafted paper pattern, although a bit on the large side (500x593px).
Source Blaq Annabiosis
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
Used the 6th circle pattern designed by Viscious-Speed to create a print that can be used for card making or scrapbooking. Save as a PDF file for the best printing option.
Source Lovinglf
A free seamless background texture that looks like a brown stone wall.
Source V. Hartikainen
From a drawing in 'Uit de geschiedenis der Heilige Stede te Amsterdam', Yohannes Sterck, 1898.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Remixed from a drawing in 'Works. Popular edition', John Ruskin, 1886.
Source Firkin
A seamless pattern recreated from an image on Pixabay. It is reminiscent of parquet flooring and is formed from a square tile, which can be recovered in Inkscape by selecting the ungrouped rectangle and using shift-alt-I together.
Source Firkin