CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
Formed from a tile based on a drawing from 'Viaggi d'un artista nell'America Meridionale', Guido Boggiani, 1895.
Source Firkin
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
From a drawing in 'The Quiver of Love', Walter Crane, 1876
Source Firkin
The rectangular tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
It’s a hole, in a pattern. On your website. Dig it!
Source Josh Green
Medium gray pattern with small strokes to give a weave effect.
Source Catherine
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Pixel by pixel, sharp and clean. Very light pattern with clear lines.
Source M.Ashok
You just can’t get enough of the fabric patterns, so here is one more for your collection.
Source Krisp Designs
Tweed is back in style – you heard it here first. Also, the @2X version here is great!
Source Simon Leo
A gray background pattern with a texture of textile. Suits perfectly for web design.
Source V. Hartikainen
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen
Gold Triangular Seamless Pattern No Background
Source GDJ
From a drawing in 'Codogno e il suo territorio nella cronaca e nella storia'', Gio and Giarella Cairo, 1897.
Source Firkin
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Polka Dots Mark II 3 No Background
Source GDJ
This background pattern has futuristic look. So, maybe it could be used on websites or blogs dedicated to video games?!
Source V. Hartikainen
Sort of like the Photoshop transparent background, but better!
Source Alex Parker
Green Web Background, Seamless tile.
Source V. Hartikainen
It’s like Shine Dotted’s sister, only rotated 45 degrees.
Source mediumidee