Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Curved Diamond Pattern 3 No Background
Source GDJ
A free background pattern with abstract green tiles.
Source V. Hartikainen
Got some felt in my mailbox today, so I scanned it for you to use.
Source Atle Mo
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Formed by distorting an image on Pixabay that was uploaded by gustavorezende. To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
After 1 comes 2, same but different. You get the idea.
Source Hendrik Lammers
A lovely light gray pattern with stripes and a dash of noise.
Source V. Hartikainen
Here's a repeatable texture that resembles a light green concrete wall or something similar.
Source V. Hartikainen
Prismatic Geometric Pattern Background 2
Source GDJ
Element of beach pattern with background.
Source Rones
Dark wooden pattern, given the subtle treatment. based on texture from Cloaks. https://cloaks.deviantart.com
Source Atle Mo
From a tile that can be had by selecting the rectangle in Inkscape and using 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
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
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
Colour version that is close to the original drawing uploaded to Pixabay by pencilparker.
Source Firkin
Remixed from a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
Farmer could be some sort of fabric pattern, with a hint of green.
Source Fabian Schultz
First pattern tailor-made for Retina, with many more to come. All the old ones are upscaled, in case you want to re-download.
Source Atle Mo
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Fix side and a seamless pattern formed from circles.
Source SliverKnight